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Journal articles on the topic 'Commutative semigroups'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

G, Ramesh, and Mahendran S. "Some Properties of Commutative Ternary Right Almost Semigroups." Indian Journal of Science and Technology 16, no. 45 (2023): 4255–66. https://doi.org/10.17485/IJST/v16i45.1937.

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Abstract <strong>Objective/Background:</strong> In this paper, the concept of commutative ternary right almost semigroups is introduced. The properties of ternary right almost semigroups and commutative ternary right almost semigroups are also discussed. Finally, regular only and the regularity are also explored in ternary right almost semigroups. <strong>Methods:</strong> Properties of ternary right almost semigroup have been employed to carry out this research work to obtain all the characterizations of commutative ternary right almost semigroups, regular and normal correspond

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2

Et. al., Dr D. Mrudula Devi. "A characterization of Commutative Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 5150–55. http://dx.doi.org/10.17762/turcomat.v12i3.2065.

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This paper deals with some results on commutative semigroups. We consider (s,.) is externally commutative right zero semigroup is regular if it is intra regular and (s,.) is externally commutative semigroup then every inverse semigroup is u – inverse semigroup. We will also prove that if (S,.) is a H - semigroup then weakly cancellative laws hold in H - semigroup. In one case we will take (S,.) is commutative left regular semi group and we will prove that (S,.) is ∏ - inverse semigroup. We will also consider (S,.) is commutative weakly balanced semigroup and then prove every left (right) regul

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3

Gigoń, Roman S. "Some results on $$\mathcal {L}$$-commutative semigroups." Semigroup Forum 101, no. 2 (2020): 385–99. http://dx.doi.org/10.1007/s00233-020-10099-1.

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Abstract We prove first that every $$\mathcal {H}$$ H -commutative semigroup is stable. Using this result [and some results from the standard text (Nagy, Special classes of semigroups, Kluwer, Dordrecht, 2001)], we give two equivalent conditions for a semigroup to be an archimedean $$\mathcal {H}$$ H -commutative semigroup containing an idempotent element. It turns out that this result can be partially extended to $$\mathcal {L}$$ L -commutative semigroups and quasi-commutative semigroups.

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4

Ahmadidelir, K., C. M. Campbell, and H. Doostie. "Almost Commutative Semigroups." Algebra Colloquium 18, spec01 (2011): 881–88. http://dx.doi.org/10.1142/s1005386711000769.

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The commutativity degree of groups and rings has been studied by certain authors since 1973, and the main result obtained is [Formula: see text], where Pr (A) is the commutativity degree of a non-abelian group (or ring) A. Verifying this inequality for an arbitrary semigroup A is a natural question, and in this paper, by presenting an infinite class of finite non-commutative semigroups, we prove that the commutativity degree may be arbitrarily close to 1. We name this class of semigroups the almost commutative or approximately abelian semigroups.

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5

Dudek, Józef, and Andrzej Kisielewicz. "Totally commutative semigroups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 3 (1991): 381–99. http://dx.doi.org/10.1017/s144678870003456x.

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AbstractA semigroup is totally commutative if each of its essentially binary polynomials is commutative, or equivalently, if in every polynomial (word) every two essential variables commute. In the present paper we describe all varieties (equational classes) of totally commutative semigroups, lattices of subvarieties for any variety, and their free spectra.

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6

Tang, Gaohua, Huadong Su, and Beishang Ren. "Commutative Zero-divisor Semigroups of Graphs with at Most Four Vertices." Algebra Colloquium 16, no. 02 (2009): 341–50. http://dx.doi.org/10.1142/s1005386709000339.

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The zero-divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. In this paper, we study commutative zero-divisor semigroups determined by graphs. We determine all corresponding zero-divisor semigroups of all simple graphs with at most four vertices.

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7

Kelarev, A. V. "The regular radical of semigroup rings of commutative semigroups." Glasgow Mathematical Journal 34, no. 2 (1992): 133–41. http://dx.doi.org/10.1017/s001708950000865x.

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A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ(R[S])

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8

Easdown, David, and Victoria Gould. "Commutative orders." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 126, no. 6 (1996): 1201–16. http://dx.doi.org/10.1017/s0308210500023362.

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A subsemigroup S of a semigroup Q is a left (right) order in Q if every q ∈ Q can be written as q = a*b(q = ba*) for some a, b ∈S, where a* denotes the inverse of a in a subgroup of Q and if, in addition, every square-cancellable element of S lies in a subgroup of Q. If S is both a left order and a right order in Q, we say that S is an order in Q. We show that if S is a left order in Q and S satisfies a permutation identity xl…xn = x1π…xnπ where 1 < 1π and nπ<n, then S and Q are commutative. We give a characterisation of commutative orders and decide the question of when one semigroup of

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9

Dekov, Deko V. "Embeddability and the word problem." Journal of Symbolic Logic 60, no. 4 (1995): 1194–98. http://dx.doi.org/10.2307/2275882.

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Let be a finitely presented variety with operations Ω and let be the variety having the same set of operations Ω but defined by the empty set of identities. A partial-algebra is a set P with a set of mappings containing for each n-ary operation f of Ω a mapping , where D ⊆ Pn. An incomplete -algebra is a partial -algebra which satisfies the defining identities of , insofar as they can be applied to the partial operations of (Trevor Evans [4, p. 67]). We call an incomplete -algebra a partial Evans-algebra if it can be embedded in a member of the variety .If the class of all partial Evans -algeb

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10

Easdown, D., and W. D. Munn. "On semigroups with involution." Bulletin of the Australian Mathematical Society 48, no. 1 (1993): 93–100. http://dx.doi.org/10.1017/s0004972700015495.

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A semigroup S with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S,.It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that t

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11

Petrich, Mario. "Normal bands of commutative cancellative semigroups revisited." International Journal of Algebra and Computation 24, no. 05 (2014): 531–51. http://dx.doi.org/10.1142/s0218196714500180.

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A semigroup S is of the type in the class of the title if S has a congruence ρ such that S/ρ is a normal band (i.e. satisfies the identities x2 = x and axya = ayxa) and all ρ-classes are commutative cancellative semigroups. We consider semigroups S with such a congruence first for completely regular semigroups, then characterize the general case in several ways, including some special cases. When S is an order in a normal band of abelian groups Q, we study the restrictions of Green's relations on Q to S. The paper concludes with the discussion of a free semigroup in the title on two generators

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12

Kelarev, A. V. "On the Jacobson radical of semigroup rings of commutative semigroups." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (1990): 429–33. http://dx.doi.org/10.1017/s0305004100069322.

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Many authors have considered the radicals of semigroup rings of commutative semigroups. A list of the papers pertaining to this field is contained in [4]. In [1] Amitsur proved that, for any associative ring R and for every free commutative semigroup S, the equalities B(RS) = B(R)S and L(RS) = L(R)S hold, where B is the Baer radical and L is the Levitsky radical. A natural problem which arises is to describe semigroup rings RS such that π(RS) = π(R)S, where π is one of the most important radicals. For the Baer and Levitsky radicals and commutative semigroups a complete solution of the above pr

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13

Farley, Reuben W. "Constructions of positive commutative semigroups on the plane, II." International Journal of Mathematics and Mathematical Sciences 8, no. 2 (1985): 321–24. http://dx.doi.org/10.1155/s0161171285000333.

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A positive semiroup is a topological semigroup containing a subsemigroupNisomorphic to the multiplicative semigroup of nonnegative real numbers, embedded as a closed subset ofE2in such a way that1is an identity and0is a zero. Using results in Farley [1] it can be shown that positive commutative semigroups on the plane constructed by the techniques given in Farley [2] cannot contain an infinite number of two dimensional groups. In this work an example of such a semigroup will be constructed which does, however, contain an infinite number of one dimensional groups. Also, some preliminary results

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14

Mazurek, Ryszard. "Commutative semigroups whose endomorphisms are power functions." Semigroup Forum 102, no. 3 (2021): 737–55. http://dx.doi.org/10.1007/s00233-021-10178-x.

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AbstractFor any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ f : S → S defined by $$f(x) = x^m$$ f ( x ) = x m is an endomorphism of S. We partly solve the Lesokhin–Oman problem of characterizing the commutative semigroups whose all endomorphisms are power functions. Namely, we prove that every endomorphism of a commutative monoid S is a power function if and only if S is a finite cyclic group, and that every endomorphism of a commutative ACCP-semigroup S with an idempotent is a power function if and only if S is a finite cyclic semigroup. Furthermor

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15

Gigoń, Roman S. "Some results on certain types of Putcha semigroups." Mathematica Slovaca 72, no. 3 (2022): 611–22. http://dx.doi.org/10.1515/ms-2022-0041.

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Abstract We shall prove a variety of results on certain types of Putcha semigroups such as: left weakly commutative semigroups, 𝓡-commutative semigroups, 𝓡𝓒-commutative semigroups, generalized conditionally commutative semigroups.

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16

Pattinasarany, Noverly Cloren. "Ideal Dalam Semigrup Ternari Komutatif." Tensor: Pure and Applied Mathematics Journal 1, no. 2 (2020): 77–82. http://dx.doi.org/10.30598/tensorvol1iss2pp77-82.

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Algebra is a branch of mathematics that deals with mathematical objects (say, numbers with no known exact value), and uses symbols such as x and y to study them. In algebra, the properties possessed by the operations that can be performed on the object (think addition and multiplication) are studied, and then become "weapons" when we are faced with a problem related to that object. In the structure of algebra, there are many theories such as groups, abelian groups, and semigroups. In semigroups only use binary operations, this makes researchers want to make research on semigroups using ternary

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17

FIRUZKUHY, A., and H. DOOSTIE. "Commuting Regularity degree of finite semigroups." Creative Mathematics and Informatics 24, no. 1 (2015): 43–47. http://dx.doi.org/10.37193/cmi.2015.01.05.

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A pair (x, y) of elements x and y of a semigroup S is said to be a commuting regular pair, if there exists an element z ∈ S such that xy = (yx)z(yx). In a finite semigroup S, the probability that the pair (x, y) of elements of S is commuting regular will be denoted by dcr(S) and will be called the Commuting Regularity degree of S. Obviously if S is a group, then dcr(S) = 1. However for a semigroup S, getting an upper bound for dcr(S) will be of interest to study and to identify the different types of non-commutative semigroups. In this paper, we calculate this probability for certain classes o

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18

OLIJNYK, A. S., V. I. SUSHCHANSKY, and J. K. SLUPIK. "INVERSE SEMIGROUPS OF PARTIAL AUTOMATON PERMUTATIONS." International Journal of Algebra and Computation 20, no. 07 (2010): 923–52. http://dx.doi.org/10.1142/s0218196710005960.

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The inverse semigroup of partial automaton permutations over a finite alphabet is characterized in terms of wreath products. The permutation conjugacy relation in this semigroup and the Green's relations are described. Criteria of primary conjugacy and conjugacy are given for certain naturally defined families of partial automaton permutations. Sufficient conditions under which an inverse semigroup admits a level transitive action are presented. We give explicit examples (monogenic inverse semigroups and some commutative Clifford semigroups) of inverse semigroups generated by finite automata.

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19

Nakwan, Kansada, Panuwat Luangchaisri, and Thawhat Changphas. "Implicative Negatively Partially Ordered Ternary Semigroups." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 4180–94. https://doi.org/10.29020/nybg.ejpam.v17i4.5511.

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In this paper, we introduce and examine the notion of implicative negatively partially ordered ternary semigroups, for short implicative n.p.o. ternary semigroup, which include an element that serves as both the greatest element and the multiplicative identity. We study the notion of implicative homomorphisms between these ternary semigroups, and have that any implicativehomomorphism is a homomorphism. Let φ : T1→T2 be an implicative homomorphism from a commutative implicative n.p.o. ternary semigroup T1 onto T2. We construct a quotient commutative implicative n.p.o. ternary semigroup T1/ρKer

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20

Kisielewicz, Andrzej, and Norbert Newrly. "Polynomial density of commutative semigroups." Bulletin of the Australian Mathematical Society 48, no. 1 (1993): 151–62. http://dx.doi.org/10.1017/s0004972700015550.

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An algebra is said to be polynomially n−dense if all equational theories extending the equational theory of the algebra with constants have a relative base consisting of equations in no more than n variables. In this paper, we investigate polynomial density of commutative semigroups. In particular, we prove that, for n > 1, a commutative semigroup is (n − 1)-dense if and only if its subsemigroup consisting of all n−factor-products is either a monoid or a union of groups of a bounded order. Moreover, a commutative semigroup is 0-dense if and only if it is a bounded semilattice. For semilatti

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21

Bonzini, C., A. Cherubini та B. Piochi. "The Least Commutative Congruence on a simple regular ω-semigroup". Glasgow Mathematical Journal 32, № 1 (1990): 13–23. http://dx.doi.org/10.1017/s0017089500009022.

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Piochi in [10] gives a description of the least commutative congruence γ of an inverse semigroup in terms of congruence pairs and generalizes to inverse semigroups the notion of solvability. The object of this paper is to give an explicit construction of λ for simple regular ω-semigroups exploiting the work of Baird on congruences on such semigroups. Moreover the connection between the solvability classes of simple regular ω-semigroups and those of their subgroups is studied.

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22

NAZARI, E., and Yu M. MOVSISYAN. "A CAYLEY THEOREM FOR THE MULTIPLICATIVE SEMIGROUP OF A FIELD." Journal of Algebra and Its Applications 11, no. 02 (2012): 1250042. http://dx.doi.org/10.1142/s021949881100566x.

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Since there exist two commutative elementarily equivalent semigroups of which one is the multiplicative semigroup of a field and the other is not a multiplicative semigroup of any field, it is impossible to characterize multiplicative semigroups of fields by formulas of the first order language (logic). In this work we characterize the multiplicative semigroup of a field by its binary representation (Cayley type theorem).

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23

Bulatov, Andrei, Marcin Kozik, Peter Mayr, and Markus Steindl. "The subpower membership problem for semigroups." International Journal of Algebra and Computation 26, no. 07 (2016): 1435–51. http://dx.doi.org/10.1142/s0218196716500612.

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Fix a finite semigroup [Formula: see text] and let [Formula: see text] be tuples in a direct power [Formula: see text]. The subpower membership problem (SMP) asks whether [Formula: see text] can be generated by [Formula: see text]. If [Formula: see text] is a finite group, then there is a folklore algorithm that decides this problem in time polynomial in [Formula: see text]. For semigroups this problem always lies in PSPACE. We show that the [Formula: see text] for a full transformation semigroup on [Formula: see text] or more letters is actually PSPACE-complete, while on [Formula: see text] l

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24

LAWSON, M. V. "NON-COMMUTATIVE STONE DUALITY: INVERSE SEMIGROUPS, TOPOLOGICAL GROUPOIDS AND C*-ALGEBRAS." International Journal of Algebra and Computation 22, no. 06 (2012): 1250058. http://dx.doi.org/10.1142/s0218196712500580.

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We study a non-commutative generalization of Stone duality that connects a class of inverse semigroups, called Boolean inverse ∧-semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper is given over to showing that Boolean inverse ∧-semigroups arise as completions of inverse ∧-semigroups we call pre-Boolean. An inverse ∧-semigroup is pre-Boolean if and only if every tight filter is an ultrafilter, where tight filters are defined by combining ideas of both Exel and Lenz. A simple necessary condition for a semigroup to be pre-Boolean is derived an

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25

Okniński, J., and P. Wauters. "Radicals of semigroup rings of commutative semigroups." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (1986): 435–45. http://dx.doi.org/10.1017/s0305004100064380.

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In this paper we determine radicals of semigroup rings R[S] where R is an associative, not necessarily commutative, ring and S is a commutative semigroup. We will restrict ourselves to the prime radical P, the Levitzki radical L and the Jacobson radical J. At the end we will also give a few comments on the Brown-McCoy radical U.

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26

POP, ADINA, and MARIA S. POP. "Semiprimary n−semigroups." Carpathian Journal of Mathematics 28, no. 1 (2012): 127–32. http://dx.doi.org/10.37193/cjm.2012.01.06.

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The study of commutative primary semigroups was initiated by M. Satyanarayana [?], continued by H. Lal [?] on semiprimary semigroup and generalized in the noncommutative case by S. Bogdanovic [ ´ ?], [?]. The purpose of this paper is to give a generalization of the semiprimary semigroups by replacing the binary operation by an n−ary operation, n ∈ N, n > 2. Most of the results of this paper are obtained by using the concept of radical of an ideal in an n−semigroup.

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27

Gavrylkiv, V. M. "Superextensions of cyclic semigroups." Carpathian Mathematical Publications 5, no. 1 (2013): 36–43. http://dx.doi.org/10.15330/cmp.5.1.36-43.

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Given a cyclic semigroup $S$ we study right and left zeros, singleton left ideals, the minimal ideal, left cancelable and right cancelable elements of superextensions $\lambda(S)$ and characterize cyclic semigroups whose superextensions are commutative.

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28

Łukasik, Radosław. "D’Alembert’s and Wilson’s equations on semigroups." Aequationes mathematicae 94, no. 6 (2020): 1269–79. http://dx.doi.org/10.1007/s00010-020-00708-3.

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Abstract In this paper we consider a generalization of d’Alembert’s equation and Wilson’s equation on commutative semigroups using only the semigroup operation, ie. we consider the functional equation $$\begin{aligned}&h(x+2y)+h(x)=2f(y)h(x+y),\ x,y\in S, \end{aligned}$$ h ( x + 2 y ) + h ( x ) = 2 f ( y ) h ( x + y ) , x , y ∈ S , where $$f,h:S\rightarrow \mathbb {K}$$ f , h : S → K , $$(S,+)$$ ( S , + ) is a commutative semigroup, $$\mathbb {K}$$ K is a quadratically closed field, $$\text {char}\,\mathbb {K}\ne 2$$ char K ≠ 2 .

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Stevanović, Nebojša, and Petar V. Protić. "Structure of Weakly Externally Commutative Semigroups." Algebra Colloquium 13, no. 03 (2006): 441–46. http://dx.doi.org/10.1142/s1005386706000381.

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In this paper, we deal with the concept of weakly externally commutative semigroups. We give some basic properties of weakly externally commutative semigroups and describe them as various extensions of commutative semigroups.

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30

Kelarev, A. V. "Radicals of semigroup rings of commutative semigroups." Semigroup Forum 48, no. 1 (1994): 1–17. http://dx.doi.org/10.1007/bf02573649.

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Kelarev, A. V. "On semigroup algebras of cancellative commutative semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 1-2 (1991): 1–3. http://dx.doi.org/10.1017/s0308210500028833.

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Shoji, Kunitaka. "Commutative Semigroups Which Are Semigroup Amalgamation Bases." Journal of Algebra 238, no. 1 (2001): 1–50. http://dx.doi.org/10.1006/jabr.2000.8614.

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.., Vasantha, Ilanthenral Kandasamy, and Florentin Smarandache. "NeutroAlgebra of Substructures of the Semigroups built using Zn and Z+." International Journal of Neutrosophic Science 18, no. 3 (2022): 135–56. http://dx.doi.org/10.54216/ijns.1803012.

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For the first-time authors study the NeutroAlgebraic structures of the substructures of the semigroups, { , ×}, { , ×} and { , +} where = {1, 2, …, ¥}. The three substructures of the semigroup studied in the context of NeutroAlgebra are subsemigroups, ideals and groups. The substructure group has meaning only if the semigroup under consideration is a Smarandache semigroup. Further in this paper, all semigroups are only commutative. It is proved the NeutroAlgebraic structure of ideals (and subsemigroups) of a semigroup can be AntiAlgebra or NeutroAlgebra in the case of infinite semigroups built

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Banakh, Taras, and Myroslava Vovk. "Categorically Closed Unipotent Semigroups." Axioms 11, no. 12 (2022): 682. http://dx.doi.org/10.3390/axioms11120682.

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Let C be a class of T1 topological semigroups, containing all Hausdorff zero-dimensional topological semigroups. A semigroup X is C-closed if X is closed in any topological semigroup Y∈C that contains X as a discrete subsemigroup; X is injectively C-closed if for any injective homomorphism h:X→Y to a topological semigroup Y∈C the image h[X] is closed in Y. A semigroup X is unipotent if it contains a unique idempotent. It is proven that a unipotent commutative semigroup X is (injectively) C-closed if and only if X is bounded and nonsingular (and group-finite). This characterization implies that

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HINDMAN, NEIL, and DONA STRAUSS. "Bases for commutative semigroups and groups." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 3 (2008): 579–86. http://dx.doi.org/10.1017/s0305004108001539.

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AbstractA base for a commutative semigroup (S, +) is an indexed set 〈xt〉t∈A in S such that each element x ∈ S is uniquely representable as Σt∈Fxt where F is a finite subset of A and, if S has an identity 0, then 0 = Σn∈Øxt. We investigate those commutative semigroups or groups which have a base. We obtain the surprising result that has a base. More generally, we show that an abelian group has a base if and only if it has no elements of odd finite order.

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Quinn-Gregson, Thomas. "Homogeneity of inverse semigroups." International Journal of Algebra and Computation 28, no. 05 (2018): 837–75. http://dx.doi.org/10.1142/s0218196718500376.

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An inverse semigroup [Formula: see text] is a semigroup in which every element has a unique inverse in the sense of semigroup theory, that is, if [Formula: see text] then there exists a unique [Formula: see text] such that [Formula: see text] and [Formula: see text]. We say that a countable inverse semigroup [Formula: see text] is a homogeneous (inverse) semigroup if any isomorphism between finitely generated (inverse) subsemigroups of [Formula: see text] extends to an automorphism of [Formula: see text]. In this paper, we consider both these concepts of homogeneity for inverse semigroups, and

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Li, Gang, and Jong Kyu Kim. "Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space." Abstract and Applied Analysis 5, no. 3 (2000): 147–58. http://dx.doi.org/10.1155/s1085337500000312.

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We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lipschitzian mappings with nonconvex domains in a Hilbert space.

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Bodor, Bertalan, Erkko Lehtonen, Thomas Quinn-Gregson, and Nikolaas Verhulst. "HS-stability and complex products in involution semigroups." Semigroup Forum 103, no. 2 (2021): 395–413. http://dx.doi.org/10.1007/s00233-021-10213-x.

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AbstractWhen does the complex product of a given number of subsets of a group generate the same subgroup as their union? We answer this question in a more general form by introducing HS-stability and characterising the HS-stable involution subsemigroup generated by a subset of a given involution semigroup. We study HS-stability for the special cases of regular $${}^{*}$$ ∗ -semigroups and commutative involution semigroups.

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Damag, Faten H., Amin Saif та Adem Kiliçman. "φ−Hilfer Fractional Cauchy Problems with Almost Sectorial and Lie Bracket Operators in Banach Algebras". Fractal and Fractional 8, № 12 (2024): 741. https://doi.org/10.3390/fractalfract8120741.

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In the theory of Banach algebras, we use the Schauder fixed-point theorem to obtain some results that concern the existence property for mild solutions of fractional Cauchy problems that involve the Lie bracket operator, the almost sectorial operator, and the φ−Hilfer derivative operator. For any Banach algebra and in two types of non-compact associated semigroups and compact associated semigroups, we prove some properties of the existence of these mild solutions using the Hausdorff measure of a non-compact associated semigroup in the collection of bounded sets. That is, we obtain the existenc

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Chung, Jaeyoung, and Prasanna K. Sahoo. "Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/463918.

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LetSbe a nonunital commutative semigroup,σ:S→San involution, andCthe set of complex numbers. In this paper, first we determine the general solutionsf,g:S→Cof Wilson’s generalizations of d’Alembert’s functional equations fx+y+fx+σy=2f(x)g(y)andfx+y+fx+σy=2g(x)f(y)on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.

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Puczyłowski, Edmund R. "Radicals of semigroup algebras of commutative and cancellative semigroups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 103, no. 3-4 (1986): 317–23. http://dx.doi.org/10.1017/s0308210500018965.

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SynopsisThe shape of radicals of semigroups algebras of commutative and cancellative semigroups is studied. The questions asto when a radical of those algebras is homogeneous and if homogeneous radicals have more regular form are examined.

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KISIELEWICZ, ANDRZEJ. "COMPLEXITY OF SEMIGROUP IDENTITY CHECKING." International Journal of Algebra and Computation 14, no. 04 (2004): 455–64. http://dx.doi.org/10.1142/s0218196704001840.

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We consider the [Formula: see text] problem, whose instance is a finite semigroup S and an identity I, and the question is whether I is satisfied in S. We show that the question concerning computational complexity of this problem is much harder, when restricted to commutative semigroups. We provide a relatively simple proof that in general the problem is co-NP-complete, and demonstrate, using some structure theory, that for a fixed commutative semigroup the problem can be solved in polynomial time. The complexity status of the general [Formula: see text] problem remains open.

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CARBONE, RAFFAELLA. "OPTIMAL LOG-SOBOLEV INEQUALITY AND HYPERCONTRACTIVITY FOR POSITIVE SEMIGROUPS ON $M_2({\mathbb C})$." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 03 (2004): 317–35. http://dx.doi.org/10.1142/s0219025704001633.

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We study positivity and contractivity properties for semigroups on [Formula: see text], compute the optimal log-Sobolev constant and prove hypercontractivity for the class of positive semigroups leaving invariant both subspaces generated by the Pauli matrices σ0, σ3 and σ1, σ2. The optimal log-Sobolev constant turns out to be bigger than the usual one arising in several commutative and noncommutative contexts when the semigroup acts on the off-diagonal matrices faster than on diagonal matrices. These results are applied to the semigroup of the Wigner–Weisskopf atom.

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RAJARAMA BHAT, B. V., FRANCO FAGNOLA, and MICHAEL SKEIDE. "MAXIMAL COMMUTATIVE SUBALGEBRAS INVARIANT FOR CP-MAPS: (COUNTER-)EXAMPLES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 11, no. 04 (2008): 523–39. http://dx.doi.org/10.1142/s0219025708003269.

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We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of norm continuous semigroups on [Formula: see text] leaving a maximal commutative subalgebra invariant and show that there exist Markov CP-semigroups on Md without invariant maximal commutative subalgebras for any d > 2.

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Zhuchok, Anatolii. "Structure of relatively free n-tuple semigroups." Algebra and Discrete Mathematics 36, no. 1 (2023): 109–28. http://dx.doi.org/10.12958/adm2173.

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An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion was considered by Koreshkov in the context of the theory of n-tuple algebras of associative type. The n>1 pairwise interassociative semigroups give rise to an n-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of n-tuple semigroups. We present the constructions of the free n-tuple semigroup, the free commutative n-tuple semigroup, the free rectangular n-tuple semigroup, the free left (right) k-nilpotent n-tuple semigroup, the free k-

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Fan, Yushuang, Alfred Geroldinger, Florian Kainrath, and Salvatore Tringali. "Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules." Journal of Algebra and Its Applications 16, no. 12 (2017): 1750234. http://dx.doi.org/10.1142/s0219498817502346.

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Let [Formula: see text] be a commutative semigroup with unit element such that every non-unit can be written as a finite product of irreducible elements (atoms). For every [Formula: see text], let [Formula: see text] denote the set of all [Formula: see text] with the property that there are atoms [Formula: see text] such that [Formula: see text] (thus, [Formula: see text] is the union of all sets of lengths containing [Formula: see text]). The Structure Theorem for Unions states that, for all sufficiently large [Formula: see text], the sets [Formula: see text] are almost arithmetical progressi

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JACKSON, MARCEL. "DUALISABILITY OF FINITE SEMIGROUPS." International Journal of Algebra and Computation 13, no. 04 (2003): 481–97. http://dx.doi.org/10.1142/s0218196703001535.

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We describe the inherently non-dualisable finite algebras from some semigroup related classes. The classes for which this problem is solved include the variety of bands, the pseudovariety of aperiodic monoids, commutative monoids, and (assuming a reasonable conjecture in the literature) the varieties of all finite monoids and finite inverse semigroups. The first example of an inherently non-dualisable entropic algebra is also presented.

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CAMPBELL, C. M., E. F. ROBERTSON, N. RUŠKUC, and R. M. THOMAS. "ON SUBSEMIGROUPS AND IDEALS IN FREE PRODUCTS OF SEMIGROUPS." International Journal of Algebra and Computation 06, no. 05 (1996): 571–91. http://dx.doi.org/10.1142/s0218196796000325.

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Subsemigroups and ideals of free products of semigroups are studied with respect to the properties of being finitely generated or finitely presented. It is proved that the free product of any two semigroups, at least one of which is nontrivial, contains a two-sided ideal which is not finitely generated as a semigroup, and also contains a subsemigroup which is finitely generated but not finitely presented. By way of contrast, in the free product of two trivial semigroups, every subsemigroup is finitely generated and finitely presented. Further, it is proved that an ideal of a free product of fi

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Anderson, D. D., and Victor Camillo. "Annihilator-semigroup rings." Tamkang Journal of Mathematics 34, no. 3 (2003): 223–29. http://dx.doi.org/10.5556/j.tkjm.34.2003.313.

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Let $ R $ be a commutative ring with 1. We define $ R $ to be an annihilator-semigroup ring if $ R $ has an annihilator-Semigroup $ S $, that is, $ (S, \cdot) $ is a multiplicative subsemigroup of $ (R, \cdot) $ with the property that for each $ r \in R $ there exists a unique $ s \in S $ with $ 0 : r = 0 : s $. In this paper we investigate annihilator-semigroups and annihilator-semigroup rings.

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Kehayopulu, Niovi, and Michael Tsingelis. "Noetherian and Artinian ordered groupoids—semigroups." International Journal of Mathematics and Mathematical Sciences 2005, no. 13 (2005): 2041–51. http://dx.doi.org/10.1155/ijmms.2005.2041.

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Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (semigroups) which are about to be introduced are particularly versatile. These satisfy a certain finiteness condition, namely, that every ideal of the ordered groupoid (semigroup) is finitely generated.

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