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Algebras With Vanishing n-Cohomology Groups

Published online by Cambridge University Press:  22 January 2016

Masatoshi Ikeda ,
Hiroshi Nagao  and
Tadashi Nakayama
Masatoshi Ikeda
Affiliation:
Osaka University, Osaka City University, Nagoya University
Hiroshi Nagao
Affiliation:
Osaka University, Osaka City University, Nagoya University
Tadashi Nakayama
Affiliation:
Osaka University, Osaka City University, Nagoya University
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Cohomology theory for (associative) algebras was first established in general higher dimensionalities by G. Hochschild [3], [4], [5]. Algebras with vanishing 1-cohomology groups are separable semisimple algebras ([3], Theorem 4.1). On extending and refining our recent results [6], [8], [12], we establish in the present paper the following:

Let n ≧ 2. Let A be an (associative) algebra (of finite rank) possessing a unit element 1 over a field Ω, and N be its radical.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 7 , June 1954 , pp. 115 - 131
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1954

References

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