Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-29T21:30:34.000Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[4] Nakayama, S. Eilenberg-T., On the dimension of modules and algebras II, Nagoya Math. J. 9 (1955), 1–16.Google Scholar
[6] Hirata, K., On relative homological algebra of Frobenius extensions, Nagoya Math. J. 15 (1959), 17–28.Google Scholar
[10] Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann. 127 (1954), 453–474.Google Scholar
[13] Tsuzuku, T. Nakayama-T., A remark on Frobenius extensions and endomorphism rings, Nagoya Math. J. 15 (1959), 9–16.Google Scholar
[14] Curtis, C., Quasi-Frobenius rings and Galois theory, III. J. Math. 3 (1959), 134–144.Google Scholar
[15] Hall, M., A type of algebraic closure, Ann. Math. 40 (1939), 360–369.Google Scholar
[16] Ikeda, M., On a theorem of Gaschütz, Osaka Math. J. 5 (1953), 53–58.Google Scholar
[17] Nakayama, T., On Frobeniusean algebras I, Ann. Math. 40 (1939), 611–633.Google Scholar
[18] Nakayama, T., Galois theory of simple rings, Trans. Amer. Math. Soc. 73 (1952), 276–292.Google Scholar