Title

Rings with (R, R, R) and [R,(R, R, R)] in the left nucleus

Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

1996

Journal or Book Title

Tamkang Journal of Mathematics

Volume

27

Issue

2

First Page

185

Last Page

187

Abstract

Let R be a nonassociative ring, and N = (R, R, R) + [R, (R, R, R)). We show that W = {wEN I Rw + wR + R(wR) C N} is a two-sided ideal of R. If for some rER, any one of the sets (r, R, R), (R, r, R) or (R, R, r) is contained in W, then the other two sets are contained in W also. If the associators are assumed to be contained in either the left, the middle, or the right nucleus, and I is the ideal generated by all associators, then 12 C W. If N is assumed to be contained in the left or the right nucleus, then W 2 = 0. We conclude that if R is semiprime and N is contained in the left or the right nucleus, then R is associative. We assume characteristic not 2.

Comments

This article is published as Hentzel, I. R., and Chen-Te Yen. "Rings with (R, R, R) and [R,(R, R, R)] in the left nucleus." Tamkang Journal of Mathematics vol. 27, no. 2 (1996): 185-187. Posted with permission.

Copyright Owner

Tamkang University Press

Language

en

File Format

application/pdf

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