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The Centers of Semi-Simple Algebras over a Commutative Ring

Published online by Cambridge University Press:  22 January 2016

Shizuo Endo  and
Yutaka Watanabe
Shizuo Endo
Affiliation:
Tokyo University of Education
Yutaka Watanabe
Affiliation:
Tokyo University of Education
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Recently A. Hattori introduced in [7], [8], [9] the notion of simple algebras over a commutative ring. Especially, in [9], he examined, as a fundamental problem on simple algebras, whether a directly indecomposable semi-simple algebra is simple or not and gave affirmative answers to this in some particular cases. In this note we shall first prove, as a complete answer to this, that any directly indecomposable semi-simple algebra over a Noetherian ring is simple.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 285 - 293
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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