Author:
Endo Shizuo,Watanabe Yutaka
Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference11 articles.
1. Simple algebras over a complete local ring;Watanabe;Osaka Math. J.,1966
2. Semisimple algebras over a commutative ring;Hattori;Proc. Symp. Algebra. Math. Soc. Japan,1965
3. Semisimple algebras over a commutative ring
4. Des catégories abéliennes
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