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On the Dimension of Modules and Algebras, I

Published online by Cambridge University Press:  22 January 2016

Samuel Eilenberg
Affiliation:
Columbia University
Masatoshi Ikeda
Affiliation:
Osaka University
Tadasi Nakayama
Affiliation:
Nagoya University
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In [5], Ikeda-Nagao-Nakayama gave a characterization of algebras of cohomological dimension ≦n In a subsequent paper [4] Eilenberg gave an alternative treatment of the same question. The present paper is devoted to the discussion of a number of questions suggested by the results of [4] and [5]. Among others it is shown that the conditions employed in stating the main results in [4] and [5] are equivalent, so that the main results of these two papers are in accord. Further, the cohomological dimension of a residue-algebra is studied in terms of that of the original algebra and the (module-) dimension of the associated ideal. The terminology and notation employed here are that of [3].

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

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