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On the commutativity of near-rings III

Published online by Cambridge University Press:  17 April 2009

Steve Ligh
Steve Ligh
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana, USA.
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Abstract

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Part of the recent work on near-rings has been concerned with sufficient conditions for near-rings to be commutative. Recently Howard E. Bell proved that if a d.g. near-ring R has an identity and for each x, y in R, there exists an n(x, y) > 1, such that (xy−yx)n(x, y) = xy − yx, then R is a commutative ring. In this paper we drop the requirement that R has an identity and show that the other condition is sufficient (and necessary) for R to be commutative. The inspiration for an important lemma, comes from a result of B.H. Neumann.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 3 , June 1972 , pp. 459 - 464
Copyright
Copyright © Australian Mathematical Society 1972

References

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