Results 191 to 200 of about 1,616,014 (220)
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Diophantine properties of finite commutative rings
Archive for Mathematical Logic, 2003Over some particular rings (for example, over the ring of integers, \(\mathbb{Z }\)) the main logical relations (disjunctions, conjunctions and negations) of polynomial equations admit Diophantine definitions. The main contribution of this paper is to investigate the Diophantine definability of these relations over an arbitrary finite commutative ring ...
Mihai Prunescu
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On Polynomial Functions over Finite Commutative Rings
Acta Mathematica Sinica, English Series, 2006Not every function from a commutative ring \(R\) into itself is induced by a polynomial in \(R[x]\). For certain local rings the number of functions that arise from polynomials has been determined in [\textit{S. Frisch}, Polynomial functions on finite commutative rings. Advances in commutative ring theory.
Jiang, Jianjun +3 more
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Additive cyclic codes over finite commutative chain rings [PDF]
Discrete Mathematics, 2018 Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings,
Kamil Otal +2 more
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On finiteness, commutativity, and periodicity in rings
Mathematical Journal of Okayama University, 1993The authors give new proofs for two finiteness theorems for rings. The proof of the first theorem initially proved by \textit{M. S. Putcha} and \textit{A. Yaqub} [Int. J. Math. Math. Sci. 2, 121-126 (1979; Zbl 0413.16007)] is simpler, of the second initially proved by \textit{T. Szele} [Publ. Math.
Bell, Howard E., Klein, Abraham A.
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A commutativity and finiteness condition for rings
Archiv der Mathematik, 2003In the paper under review the authors consider the following combinatorial condition on a ring \(R\): For every two infinite subsets \(X\) and \(Y\): \(XY=YX\), where for nonempty subsets \(A,B\) of \(R\), \(AB\) denotes the set \(\{ab\mid a\in A,\;b\in B\}\). Such a ring \(R\) is called a \(P_\infty\)-ring.
Bell, Howard E., Klein, Abraham A.
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The American Mathematical Monthly, 1976
(1976). Commutativity in Finite Rings. The American Mathematical Monthly: Vol. 83, No. 1, pp. 30-32.
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(1976). Commutativity in Finite Rings. The American Mathematical Monthly: Vol. 83, No. 1, pp. 30-32.
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Addendum to "Finitely Embedded Commutative Rings"
Proceedings of the American Mathematical Society, 1993This addendum to the author's paper [ibid. 112, No. 3, 657-659 (1991; Zbl 0744.13005)] supplies a reference omitted from there and proves the following consequence of its main result: A commutative ring is Artinian if and only if it is a Goldie quotient ring with nil Jacobson radical.
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Computing Primitive Idempotents in Finite Commutative Rings and Applications
Journal of Symbolic Computation, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mugurel Barcau, Vicentiu Pasol
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On the structure of finite commutative rings with an identity
Mathematical Notes of the Academy of Sciences of the USSR, 1971The author describes the structure of finite primary principal ideal rings and proves that every such ring is the factor-ring of the ring of integers of a finite extension of the field of rational \(p\)-adic numbers. He also studies the question of the number of nonisomorphic rings of this type with a fixed number of ...
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Residual Finiteness of Commutative Rings and Schemes
Canadian Journal of Mathematics, 1973This work grew out of a preliminary announcement (Notices of the Amer. Math. Soc. 18 (1971)). Here we modify the definition of residual finiteness given in [2]. This allows us, first of all, to consider a broader class of rings which are “essentially” residually finite and, secondly, to extend the notion to schemes.
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