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Rings of Quotients of Group Rings

Published online by Cambridge University Press:  20 November 2018

W. D. Burgess
W. D. Burgess*
Affiliation:
McGill University, Montreal, Quebec
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The group ring AG of a group G and a ring A is the ring of all formal sums Σg∈G agg with ag ∈ A and with only finitely many non-zero ag. Elements of A are assumed to commute with the elements of G. In (2), Connell characterized or completed the characterization of Artinian, completely reducible and (von Neumann) regular group rings ((2) also contains many other basic results). In (3, Appendix 3) Connell used a theorem of Passman (6) to characterize semi-prime group rings. Following in the spirit of these investigations, this paper deals with the complete ring of (right) quotients Q(AG) of the group ring AG. It is hoped that the methods used and the results given may be useful in characterizing group rings with maximum condition on right annihilators and complements, at least in the semi-prime case.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 865 - 875
Copyright
Copyright © Canadian Mathematical Society 1969

References

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