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Journal articles on the topic 'Monoid'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ceccherini-Silberstein, Tullio, and Michel Coornaert. "On surjunctive monoids." International Journal of Algebra and Computation 25, no. 04 (2015): 567–606. http://dx.doi.org/10.1142/s0218196715500113.

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A monoid M is called surjunctive if every injective cellular automata with finite alphabet over M is surjective. We show that all finite monoids, all finitely generated commutative monoids, all cancellative commutative monoids, all residually finite monoids, all finitely generated linear monoids, and all cancellative one-sided amenable monoids are surjunctive. We also prove that every limit of marked surjunctive monoids is itself surjunctive. On the other hand, we show that the bicyclic monoid and, more generally, all monoids containing a submonoid isomorphic to the bicyclic monoid are non-sur

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2

Kim, Hwankoo, Myeong Og Kim, and Young Soo Park. "Some Characterizations of Krull Monoids." Algebra Colloquium 14, no. 03 (2007): 469–77. http://dx.doi.org/10.1142/s1005386707000429.

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In this paper, Kaplansky-type theorems are given to characterize GCD-monoids and valuation monoids. Also, (unique) r-factorable monoids are defined and it is shown that S is a Krull monoid if and only if S is a unique t-factorable (resp., w-factorable) monoid if and only if S is a t-factorable (resp., w-factorable) t-Prüfer monoid.

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3

Lee, Edmond. "Varieties generated by 2-testable monoids." Studia Scientiarum Mathematicarum Hungarica 49, no. 3 (2012): 366–89. http://dx.doi.org/10.1556/sscmath.49.2012.3.1211.

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The smallest monoid containing a 2-testable semigroup is defined to be a 2-testable monoid. The well-known Brandt monoid B21 of order six is an example of a 2-testable monoid. The finite basis problem for 2-testable monoids was recently addressed and solved. The present article continues with the investigation by describing all monoid varieties generated by 2-testable monoids. It is shown that there are 28 such varieties, all of which are finitely generated and precisely 19 of which are finitely based. As a comparison, the sub-variety lattice of the monoid variety generated by the monoid B21 i

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4

Polo, Harold. "Approximating length-based invariants in atomic Puiseux monoids." Algebra and Discrete Mathematics 33, no. 1 (2022): 128–39. http://dx.doi.org/10.12958/adm1760.

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A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids.

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García-García, Juan Ignacio, Daniel Marín-Aragón, and Alberto Vigneron-Tenorio. "On Ideals of Submonoids of Power Monoids." Mathematics 13, no. 4 (2025): 584. https://doi.org/10.3390/math13040584.

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Let S be a numerical monoid, while a Pfin(S)-monoid S is a monoid generated by a finite number of finite non-empty subsets of S. That is, S is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. This work provides an algorithm for computing the ideals associated with some Pfin(S)-monoids. These are the key to studying some factorization properties of Pfin(S)-monoids and some additive properties of sumsets. This approach links computational commutative algebra with additive number theory.

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6

Huang, W., and J. Li. "Affinely spanned quasi-stochastic algebraic monoids." International Journal of Algebra and Computation 27, no. 08 (2017): 1061–72. http://dx.doi.org/10.1142/s0218196717500497.

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A linear algebraic monoid over an algebraically closed field [Formula: see text] of characteristic zero is called (row) quasi-stochastic if each row of each matrix element is of sum one. Any linear algebraic monoid over [Formula: see text] can be embedded as an algebraic submonoid of the maximum affinely spanned quasi-stochastic monoid of some degree [Formula: see text]. The affinely spanned quasi-stochastic algebraic monoids form a basic class of quasi-stochastic algebraic monoids. An initial study of structure of affinely spanned quasi-stochastic algebraic monoids is conducted. Among other t

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7

Cain, Alan J., and António Malheiro. "Deciding conjugacy in sylvester monoids and other homogeneous monoids." International Journal of Algebra and Computation 25, no. 05 (2015): 899–915. http://dx.doi.org/10.1142/s0218196715500241.

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We give a combinatorial characterization of conjugacy in the sylvester monoid, showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.

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8

Schwab, Emil Daniel. "Gauge Inverse Monoids." Algebra Colloquium 27, no. 02 (2020): 181–92. http://dx.doi.org/10.1142/s1005386720000152.

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The paper introduces a class of inverse (sub)monoids which contains Jones–Lawson’s gauge inverse (sub)monoid. The aim is to give examples and the basic properties of these monoids. Jones–Lawson’s gauge inverse monoid, as an inverse submonoid of the polycyclic monoid, is the prototype in our development line. The generalization leads also to Meakin–Sapir type results involving bijections between special congruences and special wide inverse submonoids.

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9

Cain, Alan J., António Malheiro, and Fábio M. Silva. "The monoids of the patience sorting algorithm." International Journal of Algebra and Computation 29, no. 01 (2019): 85–125. http://dx.doi.org/10.1142/s0218196718500649.

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The left patience sorting ([Formula: see text][Formula: see text]PS) monoid, also known in the literature as the Bell monoid, and the right patient sorting ([Formula: see text]PS) monoid are introduced by defining certain congruences on words. Such congruences are constructed using insertion algorithms based on the concept of decreasing subsequences. Presentations for these monoids are given. Each finite-rank [Formula: see text]PS monoid is shown to have polynomial growth and to satisfy a nontrivial identity (dependent on its rank), while the infinite rank [Formula: see text]PS monoid does not

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10

Behrisch, Mike, and Edith Vargas-García. "Centralising Monoids with Low-Arity Witnesses on a Four-Element Set." Symmetry 13, no. 8 (2021): 1471. http://dx.doi.org/10.3390/sym13081471.

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As part of a project to identify all maximal centralising monoids on a four-element set, we determine all centralising monoids witnessed by unary or by idempotent binary operations on a four-element set. Moreover, we show that every centralising monoid on a set with at least four elements witnessed by the Mal’cev operation of a Boolean group operation is always a maximal centralising monoid, i.e., a co-atom below the full transformation monoid. On the other hand, we also prove that centralising monoids witnessed by certain types of permutations or retractive operations can never be maximal.

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11

GABBAY, MURDOCH J., and PETER H. KROPHOLLER. "Imaginary groups: lazy monoids and reversible computation." Mathematical Structures in Computer Science 23, no. 5 (2013): 1002–31. http://dx.doi.org/10.1017/s0960129512000849.

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We use constructions in monoid and group theory to exhibit an adjunction between the category of partially ordered monoids and lazy monoid homomorphisms and the category of partially ordered groups and group homomorphisms such that the unit of the adjunction is injective. We also prove a similar result for sets acted on by monoids and groups.We introduce the new notion of a lazy homomorphism for a function f between partially ordered monoids such that f(m ○ m′) ≤ f(m) ○ f(m′).Every monoid can be endowed with the discrete partial ordering (m ≤ m′ if and only if m=m′), so our constructions provi

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12

Stepanova, A. A. "S-acts over a Well-ordered Monoid with Modular Congruence Lattice." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 87–102. http://dx.doi.org/10.26516/1997-7670.2021.35.87.

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This work relates to the structural act theory. The structural theory includes the description of acts over certain classes of monoids or having certain properties, for example, satisfying some requirement for the congruence lattice. The congruences of universal algebra is the same as the kernels of homomorphisms from this algebra into other algebras. Knowledge of all congruences implies the knowledge of all the homomorphic images of the algebra. A left $S$act over monoid $S$ is a set $A$ upon which $S$ acts unitarily on the left. In this paper, we consider $S$acts over linearly ordered and

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13

GOULD, VICTORIA. "GRAPH EXPANSIONS OF RIGHT CANCELLATIVE MONOIDS." International Journal of Algebra and Computation 06, no. 06 (1996): 713–33. http://dx.doi.org/10.1142/s0218196796000404.

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The relations ℛ* and [Formula: see text] on a monoid M are natural generalizations of Green’s relations ℛ and [Formula: see text], which coincide with ℛ and [Formula: see text] if M is regular. A monoid M in which every ℛ*-class [Formula: see text] contains an idempotent is called left (right) abundant; if in addition the idempotents of M commute, that is, E(M) is a semilattice, then M is left (right) adequate. Regular monoids are obviously left (and right) abundant and inverse monoids are left (and right) adequate. Many of the well known results of regular and inverse semigroup theory have an

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14

Gomez, Antonio Cano, and Magnus Steinby. "GENERALIZED CONTEXTS AND n-ARY SYNTACTIC SEMIGROUPS OF TREE LANGUAGES." Asian-European Journal of Mathematics 04, no. 01 (2011): 49–79. http://dx.doi.org/10.1142/s179355711100006x.

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A new type of syntactic monoid and semigroup of tree languages is introduced. For each n ≥ 1, we define for any tree language T its n-ary syntactic monoid Mn(T) and its n-ary syntactic semigroup Sn(T) as quotients of the monoid or semigroup, respectively, formed by certain new generalized contexts. For n = 1 these contexts are just the ordinary contexts (or 'special trees') and M1(T) is the syntactic monoid introduced by W. Thomas (1982,1984). Several properties of these monoids and semigroups are proved. For example, it is shown that Mn(T) and Sn(T) are isomorphic to certain monoids and semig

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15

GODELLE, EDDY. "PRESENTATION FOR RENNER MONOIDS." Bulletin of the Australian Mathematical Society 83, no. 1 (2010): 30–45. http://dx.doi.org/10.1017/s0004972710000365.

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AbstractWe extend the result obtained in E. Godelle [‘The braid rook monoid’, Internat. J. Algebra Comput.18 (2008), 779–802] to every Renner monoid: we provide a monoid presentation for Renner monoids, and we introduce a length function which extends the Coxeter length function and which behaves nicely.

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16

Zhang, Louxin. "Applying rewriting methods to special monoids." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (1992): 495–505. http://dx.doi.org/10.1017/s0305004100071176.

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A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjan[1] and Makanin[7] (see also [2]).

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17

BRANCO, MÁRIO J. J., GRACINDA M. S. GOMES, and VICTORIA GOULD. "LEFT ADEQUATE AND LEFT EHRESMANN MONOIDS." International Journal of Algebra and Computation 21, no. 07 (2011): 1259–84. http://dx.doi.org/10.1142/s0218196711006935.

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This is the first of two articles studying the structure of left adequate and, more generally, of left Ehresmann monoids. Motivated by a careful analysis of normal forms, we introduce here a concept of proper for a left adequate monoid M. In fact, our notion is that of T-proper, where T is a submonoid of M. We show that any left adequate monoid M has an X*-proper cover for some set X, that is, there is a left adequate monoid [Formula: see text] that is X*-proper, and an idempotent separating surjective morphism [Formula: see text] of the appropriate type. Given this result, we may deduce that

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18

V.K, Sreeja. "Construction of Inverse Unit Regular Monoids from a Semilattice and a Group." International Journal of Engineering & Technology 7, no. 4.36 (2018): 950. http://dx.doi.org/10.14419/ijet.v7i4.36.24927.

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This paper is a continuation of a previous paper [6] in which the structure of certain unit regular semigroups called R-strongly unit regular monoids has been studied. A monoid S is said to be unit regular if for each element s Î S there exists an element u in the group of units G of S such that s = sus. Hence where su is an idempotent and is a unit. A unit regular monoid S is said to be a unit regular inverse monoid if the set of idempotents of S form a semilattice. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempot

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19

SCHMID, WOLFGANG A. "HIGHER-ORDER CLASS GROUPS AND BLOCK MONOIDS OF KRULL MONOIDS WITH TORSION CLASS GROUP." Journal of Algebra and Its Applications 09, no. 03 (2010): 433–64. http://dx.doi.org/10.1142/s0219498810004002.

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Extensions of the notion of a class group and a block monoid associated to a Krull monoid with torsion class group are introduced and investigated. Instead of assigning to a Krull monoid only one abelian group (the class group) and one monoid of zero-sum sequences (the block monoid), we assign to it a recursively defined family of abelian groups, the first being the class group, and do alike for the block monoid. These investigations are motivated by the aim of gaining a more detailed understanding of the arithmetic of Krull monoids, including Dedekind and Krull domains, both from a technical

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20

Bardakov, Valeriy G., Slavik Jablan, and Hang Wang. "Monoid and group of pseudo braids." Journal of Knot Theory and Its Ramifications 25, no. 09 (2016): 1641002. http://dx.doi.org/10.1142/s0218216516410029.

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21

LAWSON, MARK V. "A CORRESPONDENCE BETWEEN BALANCED VARIETIES AND INVERSE MONOIDS." International Journal of Algebra and Computation 16, no. 05 (2006): 887–924. http://dx.doi.org/10.1142/s0218196706003165.

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There is a well-known correspondence between varieties of algebras and fully invariant congruences on the appropriate term algebra. A special class of varieties are those which are balanced, meaning they can be described by equations in which the same variables appear on each side. In this paper, we prove that the above correspondence, restricted to balanced varieties, leads to a correspondence between balanced varieties and inverse monoids. In the case of unary algebras, we recover the theorem of Meakin and Sapir that establishes a bijection between congruences on the free monoid with n gener

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22

GODELLE, EDDY. "THE BRAID ROOK MONOID." International Journal of Algebra and Computation 18, no. 04 (2008): 779–802. http://dx.doi.org/10.1142/s0218196708004603.

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In linear algebraic monoid theory, the Renner monoids play the role of the Weyl groups in linear algebraic group theory. It is well known that Weyl groups are Coxeter groups, and that we can associate a Hecke algebra and an Artin–Tits group to each Coxeter group. The question of the existence of a Hecke algebra associated with each Renner monoid has been positively answered. In this paper we discuss the question of the existence of an equivalent of the Artin–Tits groups in the framework of Renner monoids. We consider the seminal case of the rook monoid and introduce a new length function.

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23

FitzGerald, D. G. "A presentation for the monoid of uniform block permutations." Bulletin of the Australian Mathematical Society 68, no. 2 (2003): 317–24. http://dx.doi.org/10.1017/s0004972700037692.

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The monoid n of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation forn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice

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24

ROSALES, J. C., P. A. GARCÍA-SÁNCHEZ, and J. M. URBANO-BLANCO. "ON PRESENTATIONS OF COMMUTATIVE MONOIDS." International Journal of Algebra and Computation 09, no. 05 (1999): 539–53. http://dx.doi.org/10.1142/s0218196799000333.

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In this paper, we introduce the concept of a strongly reduced monoid and we characterize the minimal presentations for such monoids. As a consequence, we give a method to obtain a presentation for any commutative monoid.

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25

Gambo, Jeremiah Gyam, and Yohanna Tella. "A GENERALISED CENTRE OF A MONOID." International Journal of Novel Research in Computer Science and Software Engineering 10, no. 1 (2023): 22–31. https://doi.org/10.5281/zenodo.7695308.

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<strong>Abstract:</strong> In this paper, the concept of monoid was examined on a generalised setting(multiset). Denoting the generalised setting of a monoid by a multi monoid, we introduced the concept of a multi-centre of a multi monoid and study the action of a centre of a multi monoid over the mset operations on the class of finite multi monoid. Further studies revealed that even though in general, the centre of a multi monoid need not be a multi monoid, however under the class of finite commutative multi monoids, the centre of a commutative multi monoid is a multi monoid and the centre of

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GILBERT, N. D., and R. NOONAN HEALE. "THE IDEMPOTENT PROBLEM FOR AN INVERSE MONOID." International Journal of Algebra and Computation 21, no. 07 (2011): 1179–94. http://dx.doi.org/10.1142/s0218196711006893.

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We generalize the word problem for groups, the formal language of all words in the generators that represent the identity, to inverse monoids. In particular, we introduce the idempotent problem, the formal language of all words representing idempotents, and investigate how the properties of an inverse monoid are related to the formal language properties of its idempotent problem. We show that if an inverse monoid is either E-unitary or has a finite set of idempotents, then its idempotent problem is regular if and only if the inverse monoid is finite. We also give examples of inverse monoids wi

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27

Köcher, Chris, Dietrich Kuske, and Olena Prianychnykova. "The inclusion structure of partially lossy queue monoids and their trace submonoids." RAIRO - Theoretical Informatics and Applications 52, no. 1 (2018): 55–86. http://dx.doi.org/10.1051/ita/2018003.

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We model the behavior of a lossy fifo-queue as a monoid of transformations that are induced by sequences of writing and reading. To have a common model for reliable and lossy queues, we split the alphabet of the queue into two parts: the forgettable letters and the letters that are transmitted reliably. We describe this monoid by means of a confluent and terminating semi-Thue system and then study some of the monoid’s algebraic properties. In particular, we characterize completely when one such monoid can be embedded into another as well as which trace monoids occur as submonoids. Surprisingly

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FITZGERALD, D. G., and KWOK WAI LAU. "ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS." Bulletin of the Australian Mathematical Society 83, no. 2 (2010): 273–88. http://dx.doi.org/10.1017/s0004972710001851.

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AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new in

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29

EAST, JAMES. "EMBEDDINGS IN COSET MONOIDS." Journal of the Australian Mathematical Society 85, no. 1 (2008): 75–80. http://dx.doi.org/10.1017/s1446788708000153.

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AbstractA submonoid S of a monoid M is said to be cofull if it contains the group of units of M. We extract from the work of Easdown, East and FitzGerald (2002) a sufficient condition for a monoid to embed as a cofull submonoid of the coset monoid of its group of units, and show further that this condition is necessary. This yields a simple description of the class of finite monoids which embed in the coset monoids of their group of units. We apply our results to give a simple proof of the result of McAlister [D. B. McAlister, ‘Embedding inverse semigroups in coset semigroups’, Semigroup Forum

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30

Kudryavtseva, Ganna. "Two-sided expansions of monoids." International Journal of Algebra and Computation 29, no. 08 (2019): 1467–98. http://dx.doi.org/10.1142/s0218196719500590.

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We initiate the study of expansions of monoids in the class of two-sided restriction monoids and show that generalizations of the Birget–Rhodes prefix group expansion, despite the absence of involution, have rich structure close to that of relatively free inverse monoids. For a monoid [Formula: see text] and a class of partial actions of [Formula: see text], determined by a set, [Formula: see text], of identities, we define [Formula: see text] to be the universal [Formula: see text]-generated two-sided restriction monoid with respect to partial actions of [Formula: see text] determined by [For

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KAARLI, KALLE, and LÁSZLÓ MÁRKI. "A CHARACTERIZATION OF THE INVERSE MONOID OF BI-CONGRUENCES OF CERTAIN ALGEBRAS." International Journal of Algebra and Computation 19, no. 06 (2009): 791–808. http://dx.doi.org/10.1142/s021819670900538x.

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This paper provides an abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties. As a tool, a matrix construction is introduced which might be of independent interest in inverse semigroup theory. Using this construction as well as Ramsey's theorem, we embed a certain kind of inverse monoid into a factorizable monoid of the same kind. As noticed by M. Lawson, this embedding entails that the embedded finite monoids have finite F-unitary cover.

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Magid, Andy. "Differential Brauer monoids." Proceedings of the American Mathematical Society, Series B 10, no. 13 (2023): 153–65. http://dx.doi.org/10.1090/bproc/162.

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The differential Brauer monoid of a differential commutative ring R R is defined. Its elements are the isomorphism classes of differential Azumaya R R algebras with operation from tensor product subject to the relation that two such algebras are equivalent if matrix algebras over them, with entry-wise differentiation, are differentially isomorphic. The fine Bauer monoid, which is a group, is the same thing without the differential requirement. The differential Brauer monoid is then determined from the fine Brauer monoids of R R and R D R^D and the submonoid of the Brauer monoid whose underlyin

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Dubey, M. K., and S. P. Tiwari. "The Relationship Among Fuzzy Languages, Upper Sets and Fuzzy Ordered Monoids." New Mathematics and Natural Computation 15, no. 02 (2019): 361–72. http://dx.doi.org/10.1142/s1793005719500200.

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The concept of recognizability of a fuzzy language by crisp deterministic fuzzy automaton and monoid is well known. The purpose of the present work is to study the recognizability of fuzzy languages by fuzzy ordered monoids. We show that the upper sets of a given fuzzy ordered monoid play a nice role in such studies. Also, we introduce the syntactic fuzzy ordered monoid of an upper set which recognizes this upper set.

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Chen, Hui. "Characterizations of normal cancellative monoids." AIMS Mathematics 9, no. 1 (2024): 302–18. http://dx.doi.org/10.3934/math.2024018.

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<abstract><p>Normal cancellative monoids were introduced to explore the general structure of cancellative monoids, which are innovative and open up new possibilities. Specifically, we pointed out that the Green's relations in a cancellative monoid $ S $ are determined by its unitary subgroup $ U $ to a great extent. The specific composition of egg boxes in $ S $, derived from the general semigroup theory, can be settled by the subgroups of $ U $. We call a cancellative monoid normal when these subgroups are normal and characterize it as an NCM-system. This NCM-system was created in

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COJUHARI, E. P., and B. J. GARDNER. "GENERALIZED HIGHER DERIVATIONS." Bulletin of the Australian Mathematical Society 86, no. 2 (2012): 266–81. http://dx.doi.org/10.1017/s000497271100308x.

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AbstractA type of generalized higher derivation consisting of a collection of self-mappings of a ring associated with a monoid, and here called a D-structure, is studied. Such structures were previously used to define various kinds of ‘skew’ or ‘twisted’ monoid rings. We show how certain gradings by monoids define D-structures. The monoid ring defined by such a structure corresponding to a group-grading is the variant of the group ring introduced by Năstăsescu, while in the case of a cyclic group of order two, the form of the D-structure itself yields some gradability criteria of Bakhturin and

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KOUBEK, VÁCLAV, VOJTĚCH RÖDL, and BENJAMIN SHEMMER. "REPRESENTING SUBDIRECT PRODUCT MONOIDS BY GRAPHS." International Journal of Algebra and Computation 19, no. 05 (2009): 705–21. http://dx.doi.org/10.1142/s0218196709005275.

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Hedrlín and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M. In a previous paper, we give a construction G(M) for a graph with prescribed endomorphism monoid M known as a [Formula: see text]-graph. Using this construction, we derived bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. In this paper, we generalize the [Formula: see text]-graph construction and derive several new bounds for monoid classes not handled by our first paper. Among these

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KUDRYAVTSEVA, GANNA, and VOLODYMYR MAZORCHUK. "PARTIALIZATION OF CATEGORIES AND INVERSE BRAID-PERMUTATION MONOIDS." International Journal of Algebra and Computation 18, no. 06 (2008): 989–1017. http://dx.doi.org/10.1142/s0218196708004731.

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We show how one can use the partialization functor to obtain several recently defined inverse monoids, and use this functor to define new objects, which we call the inverse braid-permutation monoids. A presentation for this monoid is obtained. Finally, we study some abstract properties of the partialization functor and its iterations. This leads to a categorification of a monoid of all order-preserving maps, and series of orthodox generalizations of the symmetric inverse semigroup.

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DEIS, TIMOTHY, JOHN MEAKIN, and G. SÉNIZERGUES. "EQUATIONS IN FREE INVERSE MONOIDS." International Journal of Algebra and Computation 17, no. 04 (2007): 761–95. http://dx.doi.org/10.1142/s0218196707003755.

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It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding system of equations in the associated free group in an obvious way, but solutions to systems of equations in free groups do not necessarily lift to solutions in free inverse monoids. In this paper, we show that the problem of determining whether

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Aguiar, Marcelo, and Swapneel Mahajan. "On the Hadamard Product of Hopf Monoids." Canadian Journal of Mathematics 66, no. 3 (2014): 481–504. http://dx.doi.org/10.4153/cjm-2013-005-x.

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AbstractCombinatorial structures that compose and decompose give rise to Hopf monoids in Joyal's category of species. The Hadamard product of two Hopf monoids is another Hopf monoid. We prove two main results regarding freeness of Hadamard products. The first one states that if one factor is connected and the other is free as a monoid, their Hadamard product is free (and connected). The second provides an explicit basis for the Hadamard product when both factors are free.The first main result is obtained by showing the existence of a one-parameter deformation of the comonoid structure and appe

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ZHANG, LOUXIN. "ON THE CONJUGACY PROBLEM FOR ONE-RELATOR MONOIDS WITH ELEMENTS OF FINITE ORDER." International Journal of Algebra and Computation 02, no. 02 (1992): 209–20. http://dx.doi.org/10.1142/s021819679200013x.

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A one-relator monoid has nontrivial elements of finite order if and only if its presentation has the form (A; (PQ)mP=(PQ)nP), where PQ is a primitive word and m>n≥0. The (left-)conjugacy problem for such a monoid is shown to be reducible to the same problem for its left monoid. In particular, the (left-)conjugacy problem is decidable for the monoids M(A;(PQ)mP=(PQ)nP), where m+n≥2.

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Ateş, Firat, Eylem G. Karpuz, A. Dilek Güngör, and A. Sinan Çevik. "A NEW EXAMPLE FOR MINIMALITY OF MONOIDS." Asian-European Journal of Mathematics 03, no. 04 (2010): 531–44. http://dx.doi.org/10.1142/s1793557110000416.

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By considering the split extension of a free abelian monoid having finite rank by a finite monogenic monoid, the main purposes of this paper are to present examples of efficient monoids and, also, minimal but inefficient monoids. Although results presented in this paper seem as in the branch of pure mathematics, they are actually related to applications of Combinatorial and Geometric Group-Semigroup Theory, especially computer science, network systems, cryptography and physics etc., which will not be handled here.

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Fountain, John, and Gracinda M. S. Gomes. "PROPER COVERS OF AMPLE MONOIDS." Proceedings of the Edinburgh Mathematical Society 49, no. 2 (2006): 277–89. http://dx.doi.org/10.1017/s0013091504000070.

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AbstractProper ample monoids are described by means of a certain category acted upon on both sides by a cancellative monoid. Making use of this characterization, we show that every ample monoid $S$ has a proper ample cover, which can be taken to be finite whenever $S$ is finite.

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LOHREY, MARKUS. "DECIDABILITY AND COMPLEXITY IN AUTOMATIC MONOIDS." International Journal of Foundations of Computer Science 16, no. 04 (2005): 707–22. http://dx.doi.org/10.1142/s0129054105003248.

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Several complexity and decidability results for automatic monoids are shown: (i) there exists an automatic monoid with a P-complete word problem, (ii) there exists an automatic monoid such that the first-order theory of the corresponding Cayley-graph is not elementary decidable, and (iii) there exists an automatic monoid such that reachability in the corresponding Cayley-graph is undecidable. Moreover, it is shown that for every hyperbolic group the word problem belongs to LOGCFL, which improves a result of Cai [8].

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Crabb, M. J., and W. D. Munn. "On the l1-algebra of certain monoids." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 5 (1998): 1023–31. http://dx.doi.org/10.1017/s0308210500030043.

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The monoids considered are the free monoid Mx and the free monoid-with-involution MIx on a nonempty set X. In each case, relative to a simply-defined involution, an explicit construction is given for a separating family of continuous star matrix representations of the l1-algebra of the monoid and it is shown that this algebra admits a faithful trace. The results are based on earlier work by M. J. Crabb et al. concerning the complex semigroup algebras of Mx and MIx.

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MARGOLIS, STUART W., and JOHN C. MEAKIN. "FREE INVERSE MONOIDS AND GRAPH IMMERSIONS." International Journal of Algebra and Computation 03, no. 01 (1993): 79–99. http://dx.doi.org/10.1142/s021819679300007x.

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The relationship between covering spaces of graphs and subgroups of the free group leads to a rapid proof of the Nielsen-Schreier subgroup theorem. We show here that a similar relationship holds between immersions of graphs and closed inverse submonoids of free inverse monoids. We prove using these methods, that a closed inverse submonoid of a free inverse monoid is finitely generated if and only if it has finite index if and only if it is a rational subset of the free inverse monoid in the sense of formal language theory. We solve the word problem for the free inverse category over a graph Γ.

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GOULD, VICTORIA, and MIKLÓS HARTMANN. "Coherency, free inverse monoids and related free algebras." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 1 (2016): 23–45. http://dx.doi.org/10.1017/s0305004116000505.

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AbstractA monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is the non-additive notion corresponding to that for a ring R stating that every finitely generated submodule of every finitely presented right R-module is finitely presented. For monoids (and rings) right coherency is an important finitary property which determines, amongst other things, the existence of a model companion of the class of right S-acts (right R-modules) and hence that the class of existentially closed right S-acts (right R-modules) is axiom

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Gould, Victoria. "Coherent Monoids." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 2 (1992): 166–82. http://dx.doi.org/10.1017/s1446788700035771.

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AbstractThis paper is concerned with a new notion of coherency for monoids. A monoid S is right coherent if the first order theory of right S-sets is coherent; this is equivalent to the property that every finitely generated S-subset of every finitely presented right S-set is finitely presented. If every finitely generated right ideal of S is finitely presented we say that S is weakly right coherent. As for the corresponding situation for modules over a ring, we show that our notion of coherency is related to products of flat left S-sets, although there are some marked differences in behaviour

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Hezarjaribi Dastaki, Masoomeh, Hamid Rasouli, and Hasan Barzegar. "Characterizing Topologically Dense Injective Acts and Their Monoid Connections." Journal of Mathematics 2024 (May 27, 2024): 1–11. http://dx.doi.org/10.1155/2024/2966461.

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In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free S-act over a monoid S is topologically dense injective if and only if S is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for

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Alonso, Juan M., and Susan M. Hermiller. "Homological Finite Derivation Type." International Journal of Algebra and Computation 13, no. 03 (2003): 341–59. http://dx.doi.org/10.1142/s0218196703001407.

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In 1987, Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness condition left FP3, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with a

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Averbukh, Boris G. "A criterion of the existence of an embedding of a monothetic monoid into a topological group." Topological Algebra and its Applications 7, no. 1 (2019): 1–12. http://dx.doi.org/10.1515/taa-2019-0001.

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AbstractUsing properties of unitary Cauchy filters on monothetic monoids, we prove a criterion of the existence of an embedding of such a monoid into a topological group. The proof of the sufficiency is constructive: under the corresponding assumptions, we are building a dense embedding of a given monothetic monoid into a monothetic group.

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