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On the Dimension of Modules and Algebras, VII. Algebras with Finite-Dimensional Residue-Algebras

Published online by Cambridge University Press:  22 January 2016

J. P. Jans  and
Tadasi Nakayama
J. P. Jans
Affiliation:
Yale University, Nagoya University and The Institute for Advanced Study
Tadasi Nakayama
Affiliation:
Yale University, Nagoya University and The Institute for Advanced Study
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It was shown in Eilenberg-Nagao-Nakayama [3] (Theorem 8 and § 4) that if Ω is an algebra (with unit element) over a field K with (Ω: K) <∞ and if the cohomolgical dimension of Ω, dim Ω, is ≦ 1, then every residue-algebra of Ω has a finite cohomological dimension. In the present note we prove a theorem of converse type, which gives, when combined with the cited result, a rather complete general picture of algebras whose residue-algebras are all of finite cohomological dimension.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 11 , February 1957 , pp. 67 - 76
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

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