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Some examples of compressible group algebras and of noncompressible group algebras

Published online by Cambridge University Press:  17 April 2009

Kaoru Motose
Kaoru Motose
Affiliation:
Department of Mathematics, Faculty of Science, Hirosaki University, Hirosaki 036, Japan.
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Abstract

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A ring R with centre Z (R) is called compressible if Z (eRe) = eZ (R) e for any idempotent e of R. In this paper we shall give some examples of compressible group algebras and of noncompressible group algebras. These examples show that it is very difficult to judge the compressibility of a group algebra.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 389 - 394
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Armendariz, E.P., Koo, H.K. and Park, J.K., “Compressible group algebras”, Comm. Algebra 13 (1985), 1763–1777.CrossRefGoogle Scholar
[2]Armendariz, E.P., Koo, H.K. and Park, J.K., “Compressible endomorphism rings of projective modules”, (Preprint).Google Scholar
[3]Armendariz, E.P. and Park, J.K., “Compressible matrix rings”, Bull. Austral. Math. Soc. 30 (1984) 295–298.CrossRefGoogle Scholar
[4]Armendariz, E.P. and Park, J.K., “Compressible P.I. group algebras”, (Preprint).Google Scholar
[5]Berberian, S.K., “The center of a corner of a ring”, J. Algebra 71 (1981), 515–523.CrossRefGoogle Scholar
[6]Bergman, G.M., “Some examples of non-compressible rings”, Comm. Algebra 12 (1984), 1–8.CrossRefGoogle Scholar
[7]Curtis, C.W. and Reiner, I., Representation theory of finite groups and associative algebras (Interscience, New York, 1962).Google Scholar
[8]Jacobson, N., The structure of rings (Amer. Math. Soc., Providence, 1956).CrossRefGoogle Scholar
[9]Osima, M., “On primary decomposable group rings”, Proc. Phy.-Math. Soc. Japan (3) 24 (1943), 1–9.Google Scholar
[10]Page, A., “Handwritten note to S.K. Berberian”, (Dated 25 02 1982).Google Scholar