Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-03T08:50:40.439Z Has data issue: false hasContentIssue false
  • English
  • Français

On Absolutely Segregated Algebras

Published online by Cambridge University Press:  22 January 2016

Masatoshi Ikeda
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Cohomology groups of (associative) algebras have been introduced (for higher dimensions) and studied by G. Hochschild in his papers [2], [3] and [4]. 1-, 2-, and 3-dimensional cohomology groups are in closest connection with some classical properties of algebras. In particular, an algebra is absolutely segregated. if and only if its 2-dimensional cohomology groups are all trivial. It is thus of use and importance to determine the structure of algebras with universally vanishing 2-cohomology groups, i.e. absolutely segregated algebras; they form a class which is wider than the class of all algebras with universally vanishing 1-cohomology groups, i.e. separable algebras in the sense of the Dickson-Wed-derburn theorem.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 63 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Gaschütz, W.. Üter den Fundamentalsatz von Maschke zur Darstellungstheorie der endlichen Gruppen. Math. Z. Rd. 56 (1952).Google Scholar
[2] Hochschild, G.. On the cohomology groups of an associative algebra, Ann. of Math., Vol. 46 (1945).CrossRefGoogle Scholar
[3] Hochschild, G.. On the cohomology theory for associative algebras, Ann. of Math., 47 (1946).CrossRefGoogle Scholar
[4] Hochschild, G.. Cohomology and representations of associative algebras, Duke Math. J., Vol. 14 (1947).CrossRefGoogle Scholar
[5] Ikeda, M.. On a theorem of Gaschütz, Osaka Math. J. Vol. 5 (1953).Google Scholar
[6] Nagao, H. and Nakayama, T.. On the structure of (M 0)- and (Mu)-modules, forthcoming in Math. Z.Google Scholar
[7] Nakayama, T.. Derivation and cohomology in simple and other rings I, Duke Math. J., Vol. 19 (1952).CrossRefGoogle Scholar