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Applications of a new $ K$-theoretic theorem to soluble group rings

Authors: P. H. Kropholler, P. A. Linnell and J. A. Moody
Journal: Proc. Amer. Math. Soc. 104 (1988), 675-684
MSC: Primary 16A27; Secondary 16A08, 16A34
MathSciNet review: 964842
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Abstract: Let $ R$ be a ring and let $ G$ be a soluble group. In this situation we shall give necessary and sufficient conditions for $ RG$ to have a right Artinian right quotient ring. In the course of this work, we shall also consider the Goldie rank problem for soluble groups and record an affirmative answer to the zero divisor conjecture for soluble groups.

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Keywords: Group ring, zero divisor conjecture, Goldie rank, quotient ring, Grothendieck group
Article copyright: © Copyright 1988 American Mathematical Society

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