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On Semi-Perfect Group Rings

Published online by Cambridge University Press:  20 November 2018

W.D. Burgess
W.D. Burgess*
Affiliation:
University of Ottawa
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In what follows the notation and terminology of [7] are used and all rings are assumed to have a unity element.

The purpose of this note is to give some partial answers to the question: under which conditions on a ring A and a group G is the group ring AG semi-perfect?

For the convenience of the reader a few definitions and results will be reviewed. A ring R is called semi-perfect if R/RadR (Jacobson radical) is completely reducible and idempotents can be lifted modulo RadR (i.e., if x is an idempotent of R/RadR there is an idempotent e of R so that e + RadR = x).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 645 - 652
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Azumaya, G., On maximally central algebras. Nagoya Math. J. 2 (1950) 119–150.Google Scholar
2. Bass, H., Finitistic dimension and a homological generalization of semi-primary rings. Trans. Amer. Math. Soc. 95 (1960) 466–488.Google Scholar
3. Connell, I.G., On the group ring. Canad. J. Math. 15 (1963) 650–685.Google Scholar
4. Greco, S., Algebras over nonlocal Hensel rings. J. Algebra 8 (1968) 45–59.Google Scholar
5. Herstein, I.N., Noncommutative rings. (Mathematical Association of America, 1968).Google Scholar
6. Keye, S., Ring theoretic properties of matrix rings. Canad. Math. Bull. 10 (1967) 365–374.Google Scholar
7. Lambek, J., Lectures on rings and modules. (Blaisdell, Waltham, Mass., U. S. A., 1966).Google Scholar
8. Rudin, W. and Schneider, H., Idempotents in group rings. Duke Math. J. 31 (1964) 585–602.Google Scholar
9. Schneider, H. and Weissglass, J., Group rings, semigroup rings and their radicals. J. Algebra 5 (1967) 1–15.Google Scholar