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On Frobenius Extensions II

Published online by Cambridge University Press:  22 January 2016

Tadasi Nakayama  and
Tosiro Tsuzuku
Tadasi Nakayama
Affiliation:
Mathematical Institute, Nagoya University
Tosiro Tsuzuku
Affiliation:
Mathematical Institute, Nagoya University
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In Part I we introduced the notion of 2. Frobenius extensions of a ring, as a generalization of Kasch’s [10] Frobenius extensions and hence of classical Frobenius algebras. We proved, in I, bilinear (or sesqui-linear, rather, to follow Bourbaki’s terminology) form and scalar product characterizations of Frobenius extensions in such extended sense, generalizing Kasch’s and classical case, and then studied homological dimensions in them, generalizing and refining the results in Eilenberg-Nakayama [4] and Hirata [6]. Dual bases were considered in case of quasi-free (2.) Frobenius extensions Also the case of a semi-primary or S-ring ground ring was studied.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 19 , October 1961 , pp. 127 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

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