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Strongly Regular Extensions of Rings

Published online by Cambridge University Press:  22 January 2016

Carl Faith
Carl Faith*
Affiliation:
Mathematisches Institut, Heidelberg, Germany and Institute for Advanced Study, Princeton, N. J.
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As defined by Arens and Kaplansky [2] a ring A is strongly regular (s.r.) in case to each a∊ A there corresponds x = xa∊A depending on a such that a2x = a. In the present article a ring A is defined to be a s.r. extension of a subring B in case each a>∊A satisfies a2x-a∊B with x = xa∊A. S.r. rings are, then, s.r. extensions of each subring. A ring A which is a s.r. extension of the center has been called a ξ-ring (see Utumi [13], Drazin [3], Martindale [11], and their bibliographies).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 20 , June 1962 , pp. 169 - 183
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1962

References

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