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Commutativity for a Certain Class of Rings

Commutativity for a Certain Class of Rings We first establish the commutativity for the semiprime ring satisfying [x n , y]x r = ±y s[x, y m]y t for all x, y in R, where m, n, r, s, and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal Springer Journals

Commutativity for a Certain Class of Rings

Georgian Mathematical Journal , Volume 5 (4) – Oct 20, 2004

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Plenum Publishing Corporation
Subject
Mathematics; Mathematics, general
ISSN
1072-947X
eISSN
1572-9176
DOI
10.1023/A:1022197800695
Publisher site
See Article on Publisher Site

Abstract

We first establish the commutativity for the semiprime ring satisfying [x n , y]x r = ±y s[x, y m]y t for all x, y in R, where m, n, r, s, and t are fixed non-negative integers, and further, we investigate the commutativity of rings with unity under some additional hypotheses. Moreover, it is also shown that the above result is true for s-unital rings. Also, we provide some counterexamples which show that the hypotheses of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital.

Journal

Georgian Mathematical JournalSpringer Journals

Published: Oct 20, 2004

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