Results 1 to 10 of about 487 (71)
Amitsur's theorem, semicentral idempotents, and additively idempotent semirings
Open MathematicsThe article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation.
Rachev Martin, Trendafilov Ivan
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AxiomsThe explicit forms of idempotent and semicentral idempotent triangular matrices over an additively idempotent semiring are obtained. We define a diamond composition of idempotents and give a representation of an idempotent n×n matrix as an (n−1)th degree
Dimitrinka Vladeva
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On the Solutions of Linear Systems over Additively Idempotent Semirings
MathematicsThe aim of this article is to solve the system XA=Y, where A=(ai,j)∈Mn×m(S), Y∈Sm and X is an unknown vector of a size n, with S being an additively idempotent semiring. If the system has solutions, then we completely characterize its maximal one, and in
ALVARO OTERO SANCHEZ +2 more
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Derivations in a product of additively idempotent semirings [PDF]
AIP Conference Proceedings, 2021 In this paper we introduce the notion of derivation in product (direct product) of additively idempotent semirings. These semirings are useful and important tools in diverse areas such as design of switching circuits, automata theory, information systems, dynamic programming and decision theory.
Ivan Trendafilov, Radoslav Tzvetkov
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Invertible Matrices over Finite Additively Idempotent Semirings [PDF]
Semigroup Forum, 2012 11 ...
Kendziorra, Andreas +2 more
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The variety of commutative additively and multiplicatively idempotent semirings [PDF]
Semigroup Forum, 2017 The semirings in the title are algebras \((S,+,\cdot)\) with two semilattice structures \((S,+)\) and \((S,\cdot)\), where multiplication distributes over addition. They are quite well known under the name of meet-distributive bisemilattices, or bisemilattices with one distributive law.
Ivan Chajda, Helmut Länger
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Finite simple additively idempotent semirings
Journal of Algebra, 2013 26 pages, 1 ...
Kendziorra, Andreas, Zumbrägel, Jens
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On injectivity of semimodules over additively idempotent division semirings and chain MV-semirings
Journal of Algebra, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tran Giang Nam
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The finite basis problem for additively idempotent semirings of order four, I
Semigroup ForumWe study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 of them are finitely based and the remaining ones are nonfinitely based.
Ren, Miaomiao +3 more
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The finite basis problem for additively idempotent semirings of order four, III
Semigroup ForumWe study the finite basis problem for $4$-element additively idempotent semirings whose additive reducts have two minimal elements and one coatom. Up to isomorphism, there are $112$ such algebras. We show that $106$ of them are finitely based and the remaining ones are nonfinitely based.
Ren, Miaomiao +3 more
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