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A class of regularities for rings
Published online by Cambridge University Press: 09 April 2009
Abstract
In this paper a general concept of regularity for rings is defined. It is shown that every regularity determines in a natural way a subradical and a radical for rings. A wide class of regularities is constructed: the class of polynomial regularities. All well-known regularities, such as the Perlis-Jacobson regularity, the von Neumann regularity and many others, belong to this class. Special attention is paid to regularities which are elementary in the sense that the so-called unic and nullic polynomial regularities can be thought of as intersections of the elementary ones.
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- Copyright © Australian Mathematical Society 1979
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