Vol. 36, No. 2, 1971

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Linear identities in group rings. I

Donald Steven Passman

Vol. 36 (1971), No. 2, 457–483
Abstract

Let K[G] denote the group ring of a (not necessarily finite) group G and suppose that this ring satisfies a nontrivial polynomial identity of degree n. If Δ denotes the finite conjugate subgroup of G, then we show that [G : Δ] n!. Furthermore, if K[G] is semiprime, then G has an abelian subgroup of finite bounded index.

Mathematical Subject Classification
Primary: 20.80
Milestones
Received: 25 May 1970
Published: 1 February 1971
Authors
Donald Steven Passman