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A Generalization of the Almost Zero Theory

Published online by Cambridge University Press:  22 January 2016

R. Sridharan
R. Sridharan*
Affiliation:
Tata Institute of Fundamental Research, Bombay 1
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In this note we shall give a modified definition of cohomology groups for algebras. For a class of (infinite rank) algebras (which includes Frobenius algebras, group rings of infinite groups and division algebras of countable rank over fields), these groups can be characterized in a manner similar to the cohomology groups in the * Almost Zero theory’ of B. Eckmann [2]. Actually, in the case of group rings, these coincide with the cohomology groups in the almost zero theory.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 14 , February 1959 , pp. 85 - 93
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1959

References

[1] Cartan, H. and Eilenberg, S., Homological algebra, Princeton, 1956.Google Scholar
[2] Eckmann, B., On complexes over a ring and restricted cohomology groups, Proc. Nat. Acad. Sci. 33 (1947), 275–281.Google Scholar
[3] Eilenberg, S. and Nakayama, T., On the dimension of modules and algebras II, Nagoya Math. Jour., 9 (1955), 1–16.Google Scholar
[4] Eilenberg, S., Rosenberg, A. and Zelinsky, D., On the dimension of modules and algebras VIII, Nagoya Math. Jour., 12 (1957), 71–93.Google Scholar
[5] Hochschild, G., Relative Homolo£ical Algebra, Trans. Amer. Math. Soc, 82 (1956), 246–269.Google Scholar
[6] Jacobson, N., Stucture of Rings, A.M.S. Colloq. publns.,(1956).Google Scholar