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The Centers of Semi-Simple Algebras Over a Commutative Ring, II

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo  and
Yutaka Watanabe
Shizuo Endo
Affiliation:
Tokyo University of Education, Osaka University
Yutaka Watanabe
Affiliation:
Tokyo University of Education, Osaka University
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In this note we assume that all rings have identities and denote by R a commutative ring. All R-algebras considered are assumed to be finitely generated faithful R-modules. An R-algebra Λ is said to be semi-simple ([5]), if any finitely ‘generated Λ-module is (Λ, R)-projective.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 1 - 6
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc., 97 (1960), 367–409.CrossRefGoogle Scholar
[2] Endo, S., Completely faithful modules and quasi-Frobenius algebras, J. Math. Soc. Japan, 19 (1967), 437–456.CrossRefGoogle Scholar
[3] Endo, S. and Watanabe, Y., The centers of semi-simple algebras over a commutative ring, Nagoya Math. J., 30 (1967), 285–293.Google Scholar
[4] Endo, S. and Watanabe, Y., On separable algebras over a commutative ring, Osaka J. Math., 4 (1967), 233–242.Google Scholar
[5] Hattori, A., Semi-simple algebras over a commutative ring, J. Math. Soc. Japan, 15 (1963), 404–419.CrossRefGoogle Scholar
[6] Hattori, A., Simple algebras over a commutative ring, Nagoya Math. J., 27 (1966), 611–616.Google Scholar
[7] Nagata, M., Local rings, Interscience, New York, 1962.Google Scholar