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On fully invariant ideals
of the free group algebra

Authors: A. N. Krasil'nikov and Samuel M. Vovsi
Journal: Proc. Amer. Math. Soc. 124 (1996), 2613-2618
MSC (1991): Primary 16S34, 20C07
MathSciNet review: 1343706
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Abstract: Let $RF$ be the group algebra of a free noncyclic group $F$ over an integral domain $R$. It is proved that if $R$ is not a field, then there exists a fully invariant ideal $I$ of $RF$ such $RF/I$ is torsion-free but not projective as an $R$-module. In other words, there exists a pure nonprojective variety of group representations over $R$.

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Additional Information

A. N. Krasil'nikov
Affiliation: Department of Algebra, Moscow State Pedagogical University, Moscow 119882, Russia

Samuel M. Vovsi
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540

Received by editor(s): July 18, 1994
Additional Notes: The first author’s research was partially supported by RFFR Grant 93-011-1541 and ISF Grant MID 000. This paper was prepared while the second author was visiting the Institute for Advanced Study, whose hospitality is gratefully acknowledged
Communicated by: Ronald Solomon
Article copyright: © Copyright 1996 American Mathematical Society