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: https://doi.org/10.1112/jlms/s2-11.3.369

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.

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• Item ORO ID
• 31528
• Item Type
• Journal Item
• 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 or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 1975 London Mathematical Society
• Depositing User
• Camilla Jordan