Results 201 to 210 of about 904 (238)

Commutative Rings with Finitely Generated Multiplicative Semigroup

Semigroup Forum, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anderson, D. D., Stickles, Joe
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Finite Commutative Rings and Their Applications

2002
Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject.
Bini, G, FLAMINI, FLAMINIO
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On Polynomial Functions over Finite Commutative Rings

Acta Mathematica Sinica, English Series, 2006
Not 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, Peng, Guohua, Sun, Qi, Zhang, Qifan   +3 more
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Commutativity in Finite Rings

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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Addendum to "Finitely Embedded Commutative Rings"

Proceedings of the American Mathematical Society, 1993
This 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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Finite Commutative Rings. Regular Polynomials

2002
In this chapter we want to analyze the structure of finite, commutative rings with identity. We shall prove that any such ring can be uniquely expressed as a direct sum of finite local rings.
Gilberto Bini, Flaminio Flamini
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FINITE RINGS WITH COMMUTING NILPOTENT ELEMENTS

Communications in Algebra, 1996
ABSTRACT: As a generalization of Wedderburn's theorem, Herstein [5] proved that a finite ring R is commutative, if all nilpotent elements are contained in the center of R. However a finite ring with commuting nilpotent elements is not necessarily commutative.
Yasuyuki Hirano, Takao Sumiyama
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Residual Finiteness of Commutative Rings and Schemes

Canadian Journal of Mathematics, 1973
This 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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Finite maximal chains of commutative rings

Journal of Algebra and Its Applications, 2014
Let R ⊆ S be a unital extension of commutative rings, with [Formula: see text] the integral closure of R in S, such that there exists a finite maximal chain of rings from R to S. Then S is a P-extension of R, [Formula: see text] is a normal pair, each intermediate ring of R ⊆ S has only finitely many prime ideals that lie over any given prime ideal of
Ayache, Ahmed, Dobbs, David E.
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Diophantine properties of finite commutative rings

Archive for Mathematical Logic, 2003
Over 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 ...
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