Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 47, No. 1, pp. 275288 (2006) 

Single elementsB. J. Gardner and Gordon MasonDepartment of Mathematics, University of Tasmania. Hobart, Tasmania, Australia; Department of Mathematics & Statistics, University of New Brunswick, Fredericton, N.B., CanadaAbstract: 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 Full text of the article:
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