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On Segregated Rings and Algebras

Published online by Cambridge University Press:  22 January 2016

J. P. Jans
J. P. Jans*
Affiliation:
Yale University and The Ohio State University
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Segregated algebras have been nicely characterized by M. Ikeda [4]. In this paper §1, we consider segregated rings and study the structure of such rings in Theorems 1.1 and 1.2. In §2, we specialize to the case of segregated algebras of finite dimension over a field. Theorem 2.1 gives a new characterization of such algebras. Theorem 2.2 shows an interesting property of segregated algebras; two segregated algebras S and T, with radicals N and P respectively, are isomorphic if and only if S/N2 and T/P2 are isomorphic.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 11 , February 1957 , pp. 1 - 7
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Artin, E., Nesbitt, C. J., and Thrall, R. M., Rings with Minimum Condition, University of Michigan Press 1948.Google Scholar
[2] Auslander, M., Eilenberg, S., Notes on Cohomology Theory of Groups, available from Dept. of Math., University of Chicago.Google Scholar
[3] Hochschild, G., On the Cohomology of an Associative Algebra, Ann. of Math. vol. 47 (1946).Google Scholar
[4] Ikeda, M., On Absolutely Segregated Algebras, Nagoya Math. Journal vol. 6 (1953).CrossRefGoogle Scholar