The Commutativity of a Special Class of Rings
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Published:1960
Issue:
Volume:12
Page:263-268
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ISSN:0008-414X
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Container-title:Canadian Journal of Mathematics
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language:en
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Short-container-title:Can. j. math.
Author:
Martindale Wallace S.
Abstract
A well-known theorem of Jacobson (1) states that if every element x of a ring R satisfies xn(x) = x where n(x) > 1 is an integer, then R is commutative. A series of generalizations of this theorem have been proved by Herstein (2; 3; 4; 5; 6), his last result in this direction (6) being that a ring R is commutative provided every commutator u of R satisfies un(u) = u. We now define a γ-ring to be a ring R in which un(u) — u is central for every commutator u of R (where n(u) > 1 is an integer). In the present paper we verify the following conjecture of Herstein: every commutator of a γ-ring is central.
Publisher
Canadian Mathematical Society
Subject
General Mathematics
Cited by
1 articles.
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1. H-extension of ring;Journal of the Australian Mathematical Society;1969-08