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A class of regularities for rings

Published online by Cambridge University Press:  09 April 2009

C. Roos
C. Roos
Affiliation:
Mathematical DepartmentUniversity of TechnologyDelft, Holland
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Abstract

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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 4 , June 1979 , pp. 437 - 453
Copyright
Copyright © Australian Mathematical Society 1979

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