Commutativity results for rings

Author:

Abu-Khuzam Hazar

Abstract

Let R be an associative ring. We prove that if for each finite subset F of R there exists a positive integer n = n(F) such that (xy)nyn xn is in the centre of R for every x, y in F, then the commutator ideal of R is nil. We also prove that if n is a fixed positive integer and R is an n(n + 1)-torsion-free ring with identity such that (xy)nynxn = (yx)n xnyn is in the centre of R for all x, y in R, then R is commutative.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference10 articles.

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2. A commutativity theorem

3. A note on commutativity of semiprime PI-rings;Kezlan;Math. Japon.,1982

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1. Commutativity of rings involving additive mappings;Quaestiones Mathematicae;2014-03-14

2. Commutativity conditions on rings;Bulletin of the Australian Mathematical Society;1991-08

3. Commutativity theorems for rings with polynomial constraints on certain subsets;Bulletin of the Australian Mathematical Society;1991-06

4. On commutativity of rings with some polynomial constraints;Bulletin of the Australian Mathematical Society;1990-04

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