Results 221 to 230 of about 8,103 (256)

IDEALS IN COMMUTATIVE RINGS

Mathematics of the USSR-Sbornik, 1976
This paper deals with one-dimensional (commutative) rings without nilpotent elements such that every ideal is generated by three elements. It is shown that in such rings the square of every ideal is invertible, i.e. divides its multiplier ring. In addition, every ideal is distinguished, in the sense that on localization at any maximal ideal it becomes ...
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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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Commutative Coherent Rings

Canadian Journal of Mathematics, 1982
Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to provide two new characterizations of coherent rings. The first of these characterizations shows that the class of coherent rings is precisely the class of rings for which certain duality homomorphisms are isomorphisms.
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A Commutativity Condition for Rings

Canadian Journal of Mathematics, 1976
The object of this paper is to prove the following theorem, a special case of which was previously explored in [1].THEOREM. Let R be any associative ring with the property that(†) for each x,y ∊ R, there exist integers m,n ≧ I for which xy = ymxn.
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On the commutativity of non-associative rings

Publicationes Mathematicae Debrecen, 2022
\textit{E. C. Johnsen}, \textit{D. L. Outcalt}, and \textit{A. Yaqub} proved that a (not necessarily associative) ring with identity satisfying \((xy)^2 = x^2y^2\) for all \(x,y\) is commutative [Am. Math. Mon. 75, 288--289 (1968; Zbl 0162.33602)].
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On Commuting Rings Of Endomorphisms

Canadian Journal of Mathematics, 1956
Various problems concerning the general theory of centralizers of modules which are not assumed to be completely reducible have been discussed by Fitting (3), Brauer (2), and Nakayama. In this paper we present a new approach to some of these questions, which has its origin in Weyl's discussion (15) of the centralizer of a finite group of collineations.
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On the Commutativity of a Ring with Identity

Canadian Mathematical Bulletin, 1984
AbstractLet R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R:(I)xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0;(II)xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0;(III)xmyn = ynxm and m! n! x≠0 except x = 0;(IV)(xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite ...
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A Condition for the Commutativity of Rings

Canadian Journal of Mathematics, 1957
A well-known theorem of Jacobson (1) asserts that if every element a of a ring A satisfies a relation an(a) = a where n(a) > 1 is an integer, then A is a commutative ring.
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Commutativity of rings with constraints on commutators

2000
This paper studies commutativity of rings \(R\) satisfying polynomial identities of the form\break \(x^t[x^n,y]y^r=[x,y^m]y^s\) and three similar forms, where \(n,m,r,s,t\) are suitably-chosen nonnegative integers. Whether the theorems are correct as stated is not clear, but for some \((n,m,r,s,t)\) the proofs given do not work.
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On the Commutativity of Rings with Constraints on Commutators.

International Journal of Mathematics and Computer Science
We investigate the commutativity of rings with identity satisfying identities involving commutators and their powers in the class of M!-torsion-free rings. We obtain sufficient conditions for commutativity from identities of the forms [x,y^m]=0, [x^n,y^m]=0, and [x^n,y]=[x,y^m], as well as from conditions on mappings preserving commutators.
Utsanee Leerawat, Chitlada Somsup
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