Results 221 to 230 of about 6,335 (253)

On Commutativity of Rings With Derivations

Results in Mathematics, 2002
Let \(R\) be a ring, \(S\) a nonempty subset of \(R\), and \(Z\) the center of \(R\). For \(x,y\in R\) denote \(xy- yx\) by \([x, y]\) and \(xy + yx\) by \(x\circ y\). Let \(d\) be a derivation on \(R\). For prime \(R\) and \(S\) either an ideal or a Lie ideal, the authors study commutativity under the assumption that one of the following holds for all
Ashraf, Mohammad, Nadeem-ur-Rehman
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +2 more sources

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)].
openaire   +1 more source

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.
openaire   +1 more source

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 ...
openaire   +1 more source

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.
openaire   +2 more sources

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.
openaire   +1 more source

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.
openaire   +2 more sources

Commutativity of rings with constraints on commutators

Results in Mathematics, 1985
Let F denote a commutative ring, \(F\) the corresponding ring of polynomials in two non-commuting indeterminates, and F[X,Y] the ring of polynomials in two commuting indeterminates. A polynomial \(f(X,Y)\in F\) is called admissible if each of its monomials has length at least 3 and f(X,Y) has trivial image under the natural F-algebra map from \(F\) to ...
openaire   +2 more sources