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Title: Primitive localizations of group algebras of polycyclic-by-finte groups
Authors: WAUTERS, Paul 
Issue Date: 1999
Source: Journal of algebra, 214. p. 448-457
Abstract: Let G be a polycyclic-by-finite group such that Delta(G) is torsion-free abelian and It a field. Denote by S a multiplicatively closed set of nun-zero central elements of K[G]; if K is an absolute field assume that S contains an element not in K. Our main result is when the localization K[G](S) is a primitive ring. This turns out to be equivalent to the following three conditions: (1) A = K[S, S-1] is a G-domain, (2) (Q(ZK[G]) : Q(A)) is finite, and (3) J(K[G](S)) = 0. In case G is not abelian-by-finite, condition (3) is not needed. hn immediate consequence is the following. Let K be a field; in ease K is an absolute field assume that Delta(G) not equal 1. Then K[G](ZK[G]) is a primitive ring. In the final section a class of examples is constructed. (C) 1999 Academic Press.
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ISI #: 000079685800004
Type: Journal Contribution
Validations: ecoom 2000
Appears in Collections:Research publications

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