Results 1 to 10 of about 266 (139)
Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems
Axioms, 2023 This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O.
Florin F. Nichita
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Discrete Mathematics, 1974 AbstractStudies of various algebraic structures which can be defined over a Boolean algebra by means of Boolean operations have been made by Bernstein [1, 2], Cunkle [3], Elliott [4], Frink [6, 7], Grätzer [8], Grätzer and Schmidt [9], Rudeanu [10, 11], Vaidyanathaswamy [12], Wiener [13], and others.
C. H. Cunkle, Sergiu Rudeanu
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Idempotent generated algebras and Boolean powers of commutative rings [PDF]
Algebra Universalis, 2015 For a commutative ring R, we introduce the notion of a Specker R-algebra and show that Specker R-algebras are Boolean powers of R. For an indecomposable ring R, this yields an equivalence between the category of Specker R-algebras and the category of Boolean algebras.
Guram Bezhanishvili +2 more
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Classification of Boolean algebras through von Neumann regular $\mathcal{C}^{\infty}-$rings [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper, we introduce the concept of a ``von Neumann regular $\mathcal{C}^{\infty}$-ring", which is a model for a specific equational theory.
Jean Berni, Hugo Mariano
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Equivalence between varieties of square root rings and Boolean algebras with a distinguished automorphism [PDF]
Journal of Algebra, 2006 In the paper the variety \({\mathbf R}_2\) of commutative rings with unit, of characteristic two, with the square operation (as an additional operation) is studied. It is proved that this variety is generated by the finite Galois field \({\mathbf G}{\mathbf F}(2^k)\) and that this variety is equivalent to the variety of all algebras \((B,\wedge,\vee,-,\
Díaz Varela, José Patricio
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Subsumption of the Theory of Boolean Algebras under the Theory of Rings [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 1935 Stone MH.
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Lifting Elements in Coherent Quantales [PDF]
Transactions on Fuzzy Sets and Systems, 2022 An ideal I of a ring R is a lifting ideal if the idempotents of R can be lifted modulo I. A rich literature has been dedicated to lifting ideals. Recently, new algebraic and topological results on lifting ideals have been discovered.
George Georgescu
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Partial categorification of Hopf algebras and representation theory of towers of \mathcalJ-trivial monoids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 This paper considers the representation theory of towers of algebras of $\mathcal{J} -trivial$ monoids. Using a very general lemma on induction, we derive a combinatorial description of the algebra and coalgebra structure on the Grothendieck rings $G_0 ...
Aladin Virmaux
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Big Data Mining: a Computer-Oriented Method of Working with the Semantics of Assertions
Современные информационные технологии и IT-образование, 2021 When analyzing large amounts of data with the involvement of experts of subject domain, the problem of knowledge representation arises, this problem lies in describing the semantic content of judgments with their subsequent formalization, automated ...
Galina Goremykina
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Forum of Mathematics, Sigma, 2020 We introduce a notion of complexity of diagrams (and, in particular, of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions.
SAUGATA BASU, UMUT ISIK
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