Results 1 to 10 of about 904 (238)
Commutative rings with finite quotient fields [PDF]
Communications in Algebra, 2009 We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring ...
Antonio Avilés
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On the Genus of the Idempotent Graph of a Finite Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2021 Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0.
Belsi G. Gold, Kavitha S., Selvakumar K.
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Lower bound for the Erdős-Burgess constant of finite commutative rings [PDF]
AIMS Mathematics, 2020 Let $R$ be a finite commutative unitary ring. An idempotent in $R$ is an element $e\in R$ with $e^2=e$. The Erdős-Burgess constant associated with the ring $R$ is the smallest positive integer $\ell$ such that for any given $\ell$ elements (repetitions ...
Guoqing Wang
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On generalized probability in finite commutative rings
International Electronic Journal of Algebra, 2022 Let $R$ be a finite commutative ring with unity and $x\in R$. We study the probability that the product of two randomly chosen elements (with replacement) of $R$ equals $x$. We denote this probability by $Prob_x (R)$. We determine some bounds for this probability and also obtain some characterizations of finite commutative rings based on this ...
Shafiq Ur Rehman +1 more
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γ-Dual Codes over Finite Commutative Chain Rings [PDF]
AxiomsIn this article, the notion of γ-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of γ-dual codes over finite chain rings are explored.
Hai Q. Dinh +2 more
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The Logical Complexity of Finitely Generated Commutative Rings [PDF]
International Mathematics Research Notices, 2018 AbstractWe characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with $(\mathbb{N},{+},{\times })$ if and only if the space of non-maximal prime ideals of A is nonempty and connected in the Zariski topology and the nilradical of A ...
Matthias Aschenbrenner +3 more
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ZERO-DIVISOR GRAPHS OF FINITE COMMUTATIVE RINGS: A SURVEY [PDF]
Surveys in Mathematics and its Applications, 2020 This article gives a comprehensive survey on zero-divisor graphs of finite commutative rings. We investigate the results on structural properties of these graphs.
Pradeep Singh, Vijay Kumar Bhat
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Matrix product codes over finite commutative Frobenius rings [PDF]
Designs, Codes and Cryptography, 2012 Des. Codes Cryptogr.
Yun Fan, San Ling, Hongwei Liu
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Commutative Rings Whose Finitely Generated Ideals are Quasi-Flat [PDF]
, 2017 A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutative rings for which each ideal is quasi-flat (resp. quasi-projective) is given.
François Couchot
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On the finite separability of finitely generated commutative rings [PDF]
, 2023 18 pages, in Russian ...
Stanislav Kublanovsky
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