Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16S34, 20C07

Retrieve articles in all journals with MSC (1991): 16S34, 20C07


Additional 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

DOI: https://doi.org/10.1090/S0002-9939-96-03502-2
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