On fully invariant ideals of the free group algebra
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- by A. N. Krasil’nikov and Samuel M. Vovsi
- Proc. Amer. Math. Soc. 124 (1996), 2613-2618
- DOI: https://doi.org/10.1090/S0002-9939-96-03502-2
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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 $R$.References
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Bibliographic Information
- A. N. Krasil’nikov
- Affiliation: Department of Algebra, Moscow State Pedagogical University, Moscow 119882, Russia
- Email: krasilnikov.algebra@mpgu.msk.su
- Samuel M. Vovsi
- Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
- Email: vovsi@math.ias.edu, vovsi@math.rutgers.edu
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2613-2618
- MSC (1991): Primary 16S34, 20C07
- DOI: https://doi.org/10.1090/S0002-9939-96-03502-2
- MathSciNet review: 1343706