Single Elements

Citation

Gardner, BJ and Mason, G, Single Elements, Beitrage zur Algebra und Geometrie, 47, (1) pp. 275-288. ISSN 0138-4821 (2006) [Refereed Article]

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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.