Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-15T07:22:50.369Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Results on Semi-Perfect Group Rings

Published online by Cambridge University Press:  20 November 2018

S. M. Woods
S. M. Woods*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this paper is to find necessary and sufficient conditions on a group G and a ring A for the group ring AG to be semi-perfect. A complete answer is given in the commutative case, in terms of the polynomial ring A[X] (Theorem 5.8). In the general case examples are given which indicate a very strong interaction between the properties of A and those of G. Partial answers to the question are given in Theorem 3.2, Proposition 4.2 and Corollary 4.3.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 121 - 129
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Azumaya, G., On maximally central algebras, Nagoya Math. J. 2 (1951), 119–150.Google Scholar
2. Burgess, W. D., On semi-perfect group rings, Can. Math. Bull. 12 (1969), 645–652.Google Scholar
3. Connell, I. G., On the group ring, Can. J. Math. 15 (1963), 650–685.Google Scholar
4. Mueller, B. J., On semi-perfect rings, Illinois J. Math. 14 (1970), 464–467.Google Scholar
5. Passman, D. S., Infinite group rings (Marcel Dekker, New York, 1971).Google Scholar
6. Woods, S. M., On perfect group rings, Proc. Amer. Math. Soc. 27 (1971), 49–52.Google Scholar