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Note on the Cohomology Groups of Associative Algebras

Published online by Cambridge University Press:  22 January 2016

Hirosi Nagao
Hirosi Nagao*
Affiliation:
Mathematical Instilute, Osaka University
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The cohomology theory of associative algebras has been developed by G. liochschild [1], [2], [3], and the 1-, 2-, and 3-dimensional cohomology groups have been interpreted with reference to classical notions of structure in his papers. Recently M. Ikeda has obtained, by a detailed analysis of Hochschild’s modules, an interesting structural characterization of the class of algebras whose 2-dimensional cohomology groups are all zero [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 85 - 92
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Hochschild, G., On the cohomology groups of an associative algebra, Ann. of Math., 46 (1945).Google Scholar
[2] Hochschild, G., On the cohomology theory for associative algebras, Ann. of Math., 47 (1946).Google Scholar
[3] Hochschild, G., Cohomology and representations of associative algebras, Duke Math. J., 14 (1947).Google Scholar
[4] Ikeda, M., On a theorem of Gaschiitz, Osaka Math. J., 5 (1953).Google Scholar
[5] Ikeda, M., On absolutely segregated algebras, Nagoya Math, J., vol. 6 (1953).Google Scholar
[6] Kawada, Y., On the cohomology theory of rings, J. Math. Soc. Japan, 1 (1948).Google Scholar
[7] Nagao, H. and Nakayama, T., On the structure of (M0 )- and (Ma )-modules, forthcoming in Math. Z. Google Scholar