Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 1, pp. 275-288 (2006)
B. J. Gardner and Gordon MasonDepartment of Mathematics, University of Tasmania. Hobart, Tasmania, Australia; Department of Mathematics & Statistics, University of New Brunswick, Fredericton, N.B., Canada
Abstract: In this paper we consider single elements in rings and nearrings. If $R$ is a (near)ring, $x \in R$ is called single if $axb = 0 \Rightarrow ax = 0$ or $xb = 0$. In seeking rings in which each element is single, we are led to consider $0$-simple rings, a class which lies between division rings and simple rings.
Classification (MSC2000): 16U99; 16Y30
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Electronic version published on: 9 May 2006. This page was last modified: 4 Nov 2009.