Some commutativity results for rings with two-variable constraints-Reference-Cited by-同舟云学术

Some commutativity results for rings with two-variable constraints

Published:1975 Issue:2 Volume:53 Page:280-284
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bell H. E.

Abstract

It is proved that an associative ring R R has nil commutator ideal if for each x , y ϵ R x,\;y\epsilon R , there is a polynomial p ( X ) ϵ X Z [ X ] p(X)\epsilon X{\mathbf {Z}}[X] for which x y − y p ( x ) xy - yp(x) is central. Two restrictions on the p ( X ) p(X) which guarantee commutativity are established.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1975-053-02/S0002-9939-1975-0382357-9/S0002-9939-1975-0382357-9.pdf

Reference6 articles.

1. Duo rings: Some applications to commutativity theorems;Bell, Howard E.;Canad. Math. Bull.,1968

2. On some commutativity theorems of Herstein;Bell, Howard E.;Arch. Math. (Basel),1973

3. On a theorem of Herstein;Chacron, M.;Canadian J. Math.,1969

4. A theorem on rings;Herstein, I. N.;Canad. J. Math.,1953

5. The structure of a certain class of rings;Herstein, I. N.;Amer. J. Math.,1953

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