Relevant bibliographies by topics / Semiring and lattices

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Semiring and lattices'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Semiring and lattices"

1

Sharma, Tilak Raj, and Rajesh Kumar. "Lattice Ordered G􀀀Semirings." Indian Journal Of Science And Technology 17, no. 12 (2024): 1143–47. http://dx.doi.org/10.17485/ijst/v17i12.3184.

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Objectives: The main objective of this paper is to derive some of the results of lattice ordered semirings, distributive lattice, lattice ideals and morphisms. Methods: To establish the results, we use some conditions like commutativity, simple, multiplicative idempotent, additively idempotent, and finally, use the concept of lattice ideal in semirings. Findings: First we give some examples of lattice ordered semirings and then study some results regarding lattices, distributive lattices, commutative lattice ordered semirings and finally lattice ideals and morphisms. The unique feature of this
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Chen, Yizhi, and Xianzhong Zhao. "On Decompositions of Matrices over Distributive Lattices." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/202075.

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LetLbe a distributive lattice andMn,q(L)(Mn(L), resp.) the semigroup (semiring, resp.) ofn×q(n×n, resp.) matrices overL. In this paper, we show that if there is a subdirect embedding from distributive latticeLto the direct product∏i=1m‍Liof distributive latticesL1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroupMn,q(L)(semiringMn(L), resp.) to semigroup∏i=1m‍Mn,q(Li)(semiring∏i=1m‍Mn(Li), resp.). Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains. This generalize
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Tilak, Raj Sharma, and Kumar Rajesh. "Lattice Ordered G􀀀Semirings." Indian Journal of Science and Technology 17, no. 12 (2024): 1143–47. https://doi.org/10.17485/IJST/v17i12.3184.

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Abstract <strong>Objectives:</strong>&nbsp;The main objective of this paper is to derive some of the results of lattice ordered semirings, distributive lattice, lattice ideals and morphisms.&nbsp;<strong>Methods:</strong>&nbsp;To establish the results, we use some conditions like commutativity, simple, multiplicative idempotent, additively idempotent, and finally, use the concept of lattice ideal in semirings.&nbsp;<strong>Findings:</strong>&nbsp;First we give some examples of lattice ordered semirings and then study some results regarding lattices, distributive lattices, commutative lattice o
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Chajda, Ivan, and Helmut Länger. "When does a semiring become a residuated lattice?" Asian-European Journal of Mathematics 09, no. 04 (2016): 1650088. http://dx.doi.org/10.1142/s1793557116500881.

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It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The natural question arises if the converse assertion is also true. We show that the conversion is possible provided the given semiring is, moreover, completely distributive. We characterize semirings associated to complete residuated lattices satisfying the double negation law where the assumption of complete distributivity can be omitted. A similar result is o
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Shao, Yong, and Xianzhong Zhao. "Distributive Lattices of M-Rectangular Divided-semirings." Algebra Colloquium 20, no. 02 (2013): 243–50. http://dx.doi.org/10.1142/s1005386713000217.

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In this paper, we first introduce the so-called M-rectangular divided-semirings and distributive lattices of M-rectangular divided-semirings. We then discuss the relations between such a semiring and its multiplicative semigroup. Finally, we investigate subdirect product decompositions of these semirings and obtain some interesting results.
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Nasehpour, Peyman. "On the content of polynomials over semirings and its applications." Journal of Algebra and Its Applications 15, no. 05 (2016): 1650088. http://dx.doi.org/10.1142/s0219498816500882.

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In this paper, we prove that Dedekind–Mertens lemma holds only for those semimodules whose subsemimodules are subtractive. We introduce Gaussian semirings and prove that bounded distributive lattices are Gaussian semirings. Then we introduce weak Gaussian semirings and prove that a semiring is weak Gaussian if and only if each prime ideal of this semiring is subtractive. We also define content semialgebras as a generalization of polynomial semirings and content algebras and show that in content extensions for semirings, minimal primes extend to minimal primes and discuss zero-divisors of a con
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Shao, Yong, Sinisa Crvenkovic, and Melanija Mitrovic. "Distributive lattices of Jacobson rings." Publications de l'Institut Math?matique (Belgrade) 100, no. 114 (2016): 87–93. http://dx.doi.org/10.2298/pim1614087s.

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We characterize the distributive lattices of Jacobson rings and prove that if a semiring is a distributive lattice of Jacobson rings, then, up to isomorphism, it is equal to the subdirect product of a distributive lattice and a Jacobson ring. Also, we give a general method to construct distributive lattices of Jacobson rings.
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Shao, Yong, Miaomiao Ren, Sinisa Crvenkovic, and Melanija Mitrovic. "The semiring variety generated by any finite number of finite fields and distributive lattices." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 45–51. http://dx.doi.org/10.2298/pim150404026s.

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In this paper we study the semiring variety V generated by any finite number of finite fields F1,..., Fk and two-element distributive lattice B2, i.e., V = HSP{B2, F1,..., Fk}. It is proved that V is hereditarily finitely based, and that, up to isomorphism, the two-element distributive lattice B2 and all subfields of F1,..., Fk are the only subdirectly irreducible semirings in V.
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Katsov, Yefim, Tran Giang Nam, and Jens Zumbrägel. "On simpleness of semirings and complete semirings." Journal of Algebra and Its Applications 13, no. 06 (2014): 1450015. http://dx.doi.org/10.1142/s0219498814500157.

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In this paper, we investigate various classes of semirings and complete semirings regarding the property of being ideal-simple, congruence-simple, or both. Among other results, we describe (complete) simple, i.e. simultaneously ideal- and congruence-simple, endomorphism semirings of (complete) idempotent commutative monoids; we show that the concepts of simpleness, congruence-simpleness, and ideal-simpleness for (complete) endomorphism semirings of projective semilattices (projective complete lattices) in the category of semilattices coincide iff those semilattices are finite distributive latt
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DROSTE, MANFRED, and HEIKO VOGLER. "THE CHOMSKY-SCHÜTZENBERGER THEOREM FOR QUANTITATIVE CONTEXT-FREE LANGUAGES." International Journal of Foundations of Computer Science 25, no. 08 (2014): 955–69. http://dx.doi.org/10.1142/s0129054114400176.

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Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schützenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of
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Dissertations / Theses on the topic "Semiring and lattices"

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Michalski, Burkhard. "On the lattice of varieties of almost-idempotent semirings." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2018. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-232529.

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Die Arbeit beschäftigt sich mit fast-idempotenten Halbringen, die eine Verallgemeinerung der idempotenten Halbringe darstellen. Es werden - ausgehend von Halbringen mit zwei Elementen - bis auf isomorphe Bilder sämtliche fast-idempotente Halbringe mit drei Elementen generiert, diejenigen Halbringe, die schon in durch zweielementige Halbringe erzeugten Varietäten liegen, aussortiert und die in den verbleibenden elf Halbringen gültigen Gleichungen charakterisiert. Der Verband L(IA3) der Varietäten generiert durch fast-idempotente Halbringe mit maximal drei Elementen wird mit Hilfe eines Kontexts
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Wilding, David. "Linear algebra over semirings." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/linear-algebra-over-semirings(1dfe7143-9341-4dd1-a0d1-ab976628442d).html.

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Motivated by results of linear algebra over fields, rings and tropical semirings, we present a systematic way to understand the behaviour of matrices with entries in an arbitrary semiring. We focus on three closely related problems concerning the row and column spaces of matrices. This allows us to isolate and extract common properties that hold for different reasons over different semirings, yet also lets us identify which features of linear algebra are specific to particular types of semiring. For instance, the row and column spaces of a matrix over a field are isomorphic to each others' dua
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Michalski, Burkhard [Verfasser], Udo [Akademischer Betreuer] Hebisch, Udo [Gutachter] Hebisch, and Bernhard [Gutachter] Ganter. "On the lattice of varieties of almost-idempotent semirings / Burkhard Michalski ; Gutachter: Udo Hebisch, Bernhard Ganter ; Betreuer: Udo Hebisch." Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2018. http://d-nb.info/1221070088/34.

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Michalski, Burkhard. "On the lattice of varieties of almost-idempotent semirings." Doctoral thesis, 2017. https://tubaf.qucosa.de/id/qucosa%3A23201.

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Die Arbeit beschäftigt sich mit fast-idempotenten Halbringen, die eine Verallgemeinerung der idempotenten Halbringe darstellen. Es werden - ausgehend von Halbringen mit zwei Elementen - bis auf isomorphe Bilder sämtliche fast-idempotente Halbringe mit drei Elementen generiert, diejenigen Halbringe, die schon in durch zweielementige Halbringe erzeugten Varietäten liegen, aussortiert und die in den verbleibenden elf Halbringen gültigen Gleichungen charakterisiert. Der Verband L(IA3) der Varietäten generiert durch fast-idempotente Halbringe mit maximal drei Elementen wird mit Hilfe eines Kontexts
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Kala, Vítězslav. "Algebraické podstruktury v Cm." Doctoral thesis, 2013. http://www.nusl.cz/ntk/nusl-322206.

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Title: Algebraic Substructures in ℂ Author: Vítězslav Kala Department: Department of Algebra Supervisor: Prof. RNDr. Tomáš Kepka, DrSc., Department of Algebra Abstract: We study the structure of finitely generated semirings, parasemifields and other algebraic structures, developing and applying tools based on the geom- etry of algebraic substructures of the Euclidean space ℂ . To a parasemifield which is finitely generated as a semiring we attach a certain subsemigroup of the semigroup ℕ0 (defined using elements such that + = for some ∈ and ∈ ℕ). Algebraic and geometric properties of carry imp
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Book chapters on the topic "Semiring and lattices"

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Golan, Jonathan S. "Lattice-Ordered Semirings." In Semirings and their Applications. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9333-5_21.

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"Semirings and Lattices." In Generalized Blockmodeling. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511584176.010.

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Manna, Debashree. "Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices." In Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices. IGI Global, 2017. http://dx.doi.org/10.4018/978-1-5225-0914-1.ch006.

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In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over [0, 1]. Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs.
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Conference papers on the topic "Semiring and lattices"

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Tianmin Zhu and Baomin Yu. "Multiplicative band semirings and distributive lattices." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6001714.

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Shafran, Izhak, Richard Sproat, Mahsa Yarmohammadi, and Brian Roark. "Efficient determinization of tagged word lattices using categorial and lexicographic semirings." In Understanding (ASRU). IEEE, 2011. http://dx.doi.org/10.1109/asru.2011.6163945.

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