|DOI (Digital Object Identifier) Link:||http://dx.doi.org/10.1112/jlms/s2-11.3.369|
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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, , . In particular Formanek has recently shown that group rings of free products are primitive . 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|
|Extra Information:||MR number MR0419507.
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|
|Depositing User:||Camilla Jordan|
|Date Deposited:||09 Feb 2012 11:20|
|Last Modified:||16 Feb 2012 12:45|
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