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A new characterization of commutative semiregular rings

Advances in Pure and Applied Mathematics, 2020
Peter Danchev, Mahdi Samiei
doaj   +1 more source

Derivations and commutativity of rings [PDF]

Pacific Journal of Mathematics, 1979
Chung, Lung O., Luh, Jiang, Richoux, Anthony N.   +2 more
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Commutative endomorphism rings [PDF]

Pacific Journal of Mathematics, 1973
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Injective Quotient Rings of Commutative Rings

Lecture Notes in Mathematics, 1979
INTRODUCTION In the broadest sense, this is a study of commutative rings which satisfy the (finitely) pseudo-Froben[us (or (F)PF) condition: All (finitely generated) faithful modules generate the category mod-R of all R-modules. These rings include: Pr[[fer rings, almost maximal valuation rings, self-injective rings, e.g.
Carl Faith
exaly   +2 more sources

Almost-Commutativity in Rings

Acta Mathematica Hungarica, 2002
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Bell, H. E., Klein, A. A.
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A commutativity property for rings

Journal of Algebra and Its Applications, 2015
We provide a partial answer to the following question: Assume that R is a finite ring of order s such that for every two subsets M and N of cardinalities m and n respectively, there exist x ∈ M and y ∈ N such that xy = yx. What relations among s, m, n guarantee that R is commutative?
Bell, H. E., Zarrin, M.
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Commutativity of rings with derivations

Acta Mathematica Hungarica, 2010
The authors extend a theorem of \textit{H. E. Bell} and \textit{M. N. Daif} [Acta Math. Hung. 66, No. 4, 337-343 (1995; Zbl 0822.16033)] proving that the commutativity of a unital prime ring with a non-zero derivation is equivalent to several conditions on derivations of some powers (Theorem 2.2). Under the additional assumption that the identity is in
Andima, S., Pajoohesh, H.
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ON THE COMMUTING GRAPH OF RINGS

Journal of Algebra and Its Applications, 2011
Let R be a non-commutative ring. The commuting graph of R denoted by Γ(R), is a graph with vertex set R\Z(R) and two vertices a and b are adjacent if ab = ba. It has been shown that the diameter of Γ(R)c is less than 3. For a finite ring R we show that the diameter of Γ(R)c is one if and only if R is the non-commutative ring on 4 elements.
Omidi, G. R., Vatandoost, E.
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Commutative Endomorphism Rings

Canadian Journal of Mathematics, 1971
The problem of classifying the torsion-free abelian groups with commutative endomorphism rings appears as Fuchs’ problems in [ 4 , Problems 46 and 47]. They are far from solved, and the obstacles to a solution appear formidable (see [ 4; 5 ]).
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On semivalues on commutative rings

Periodica Mathematica Hungarica, 2016
The notion of a semivalue on an arbitrary unitary commutative ring is introduced, and two fundamental theorems concerning values on fields are extended to this general context.
Nilson C. Bernardes, Dinamérico P. Pombo   +1 more
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