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Some types of Separable Extensions of Rings

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Hirata
Kazuhiko Hirata*
Affiliation:
Yamanashi University
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In [5] we defined the notion of separable extensions of a ring as a generalization of that of separable algebras. In this paper we try to introduce the notion of ‘central’ separable algebras to separable extensions. Such extensions are viewed in §2. But we do not know that it is suitable or not to call them central separable extensions. As the Morita theorem for projective generators is fundamental to examine the central separable algebras we generalize it in §1. Let R be a ring and let A and B be left R-modules. We assume that R-module B is isomorphic to a direct summand of a finite direct sum of copies isomorphic to A.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 33 , November 1968 , pp. 107 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

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