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On Relative Homological Algebra of Frobenius Extensions

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Hirata
Kazuhiko Hirata*
Affiliation:
Tokyo University of Education
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In this paper we study two features of relative homological algebra of Frobenius extensions, the one is the relative dimension and the other is the relative complete resolution. The theory of Frobenius extensions was developed by F. Kasch [4] as a generalization of Frobenius algebras. We deal with only Frobenius extensions of finite rank (see §2 for the definition).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 15 , August 1959 , pp. 17 - 28
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[1] Cartan, H.-Eilenberg, S., Homological Algebra, Princeton Univ., 1956.Google Scholar
[2] Eilenberg, S.-Nakayama, T., On the Dimension of Modules and Algebras II, Nagoya Math. J. 9 (1955).Google Scholar
[3] Hochschild, G., Relative Homological Algebra, Trans, of Amer. Math. Soc. 82 (1956).CrossRefGoogle Scholar
[4] Kasch, F., Grundlagen einer Theorie der Frobeniuserweiterungen, Math. Ann. 127 (1954).Google Scholar
[5] Nakayama, T., On the Complete Cohomology Theory of Frobenius Algebras, Osaka Math. J. 9 (1957).Google Scholar