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The Jacobson radical of the group ring of a generalised free product

Jordan, Camilla (1975). The Jacobson radical of the group ring of a generalised free product. Journal of the London Mathematical Society, 2(11) pp. 369–376.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1112/jlms/s2-11.3.369
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Abstract

A well known problem in group rings asks whether the Jacobson radical is always a nil ideal [9; Problem 15, page 132]. This has been answered in the affirmative for a number of special cases where either the ring or the group is restricted; see, for example, [3], [10]. In particular Formanek has recently shown that group rings of free products are primitive [1]. In this paper we consider the case where the group is a free product with amalgamation. We obtain two main results.

Item Type: Journal Article
Copyright Holders: 1975 London Mathematical Society
ISSN: 1469-7750
Extra Information: MR number MR0419507.

Abstract references:
1. E. Formanek, "Group rings of free products are primitive", Algebra, 26 (1973), 508-511.
3. J. A. Green and S. E. Stonehewer, "The radicals of some group algebras", Algebra, 13 (1969), 137-142.
9. D. S. Passman, Infinite group rings (Marcel Dekker, New York, 1971).
10. D. A. R. Wallace, "The Jacobson radicals of group algebras of a group and of certain normal subgroups", Math. Z., 100 (1967), 282-294.
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 31528
Depositing User: Camilla Jordan
Date Deposited: 09 Feb 2012 11:20
Last Modified: 16 Feb 2012 12:45
URI: http://oro.open.ac.uk/id/eprint/31528
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