Results 51 to 60 of about 487 (71)
Two nonfinitely based additively idempotent semirings of order four
We establish two sufficient conditions for an additively idempotent semiring to be nonfinitely based. As applications, we prove that two specific $4$-element additively idempotent semirings, $S_{(4,545)}$ and $S_{(4,634)}$, whose additive reducts are chains, have no finite basis for their identities.
Yue, Mengya, Ren, Miaomiao, Gao, Zidong
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Every additively idempotent semiring satisfying $xy\approx xz$ is finitely based
We study the finite basis problem for additively idempotent semirings satisfying the identity $xy \approx xz$. Let $\mathbf{R}$ denote the variety of all such semirings. Yue et al. (2025, Algebra Universalis, DOI:10.1007/s00012-025-00908-5) established that $\mathbf{R}$ is finitely generated.
Yue, Mengya, Ren, Miaomiao
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The Rényi Entropies Operate in Positive Semifields. [PDF]
Entropy (Basel), 2019 Valverde-Albacete FJ, Peláez-Moreno C.
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Algorithm for constructing finite idempotent cyclic semirings with commutative addition
, 2017 The paper deals with finite idempotent cyclic semirings with commutative addition. The author establishes a connection between idempotent cyclic semirings with commutative addition and ideals of nonnegative integers. An algorithm for constructing these semirings is presented .
Chuprakov, D., Chuprakov, D.
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The algebraic characterizations for a formal power series over complete strong bimonoids. [PDF]
Springerplus, 2016 Jin JH, Li CQ.
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Flat extensions of groups and limit varieties of additively idempotent semirings
Journal of Algebra, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcel Jackson, Xianzhong Zhao
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Cyclic semirings with idempotent noncommutative addition
Journal of Mathematical Sciences, 2012The article discusses the structure of cyclic semirings with noncommutative addition. In the infinite case, the addition is idempotent and is either left or right. Addition of a finite cyclic semirings can be either idempotent or nonidempotent. In the finite additively idempotent cyclic semiring, addition is reduced to the addition of a cyclic ...
Evgenii M Vechtomov
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Prime congruences of additively idempotent semirings and a Nullstellensatz for tropical polynomials
Selecta Mathematica, New Series, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kalina Mincheva
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On semimodules over commutative, additively idempotent semirings
Semigroup Forum, 2001Let \((S,+,\cdot)\) be a commutative and additively idempotent semiring with absorbing zero and identity. A (right) \(S\)-semimodule \(P_S\) is projective if for any \(S\)-semimodules \(M_S\) and \(N_S\), any surjective \(S\)-homomorphism \(\varphi\colon M_S\to N_S\) and any \(S\)-homomorphism \(\psi\colon P_S\to N_S\), there exists an \(S ...
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