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On S-Rings in the Sense of F. Kasch

Published online by Cambridge University Press:  22 January 2016

Kiiti Morita*
Affiliation:
Department of Mathematics, Tokyo University of Education
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The notion of S-rings was introduced by F. Kasch [4] in establishing a theory of Frobenius extensions. S-rings possess several remarkable properties, although they have been shown to be not indispensable to the theory of Frobenius extensions. The purpose of this paper is to give some characteristic properties of S-rings.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc, 95 (1960), 466488.Google Scholar
[2] Ikeda, M., Some generalizations of quasi-Frobenius rings, Osaka Math. J., 3 (1951), 227238.Google Scholar
[3] Jans, J. P., Duality in Noetherian rings, Proc. Amer. Math. Soc, 12 (1961), 829835.Google Scholar
[4] Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann., 127 (1954), 453474.Google Scholar
[5] Kawada, Yutaka, A generalization of Morita’s theorem concerning generalized uniserial algebras, Proc. Japan Acad., 34 (1958), 404406.Google Scholar
[6] Morita, K., Duality for modules and its applications to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, vol. 6, No. 150 (1958), 83142.Google Scholar
[7] Nakayama, T. and Tsuzuku, T., On Frobenius extensions. I, Nagoya Math. J., 17 (1960), 89110.CrossRefGoogle Scholar