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On fully invariant ideals of the free group algebra
Author(s):
A.
N.
Krasil'nikov;
Samuel
M.
Vovsi
Journal:
Proc. Amer. Math. Soc.
124
(1996),
2613-2618.
MSC (1991):
Primary 16S34, 20C07
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Abstract:
Let  be the group algebra of a free noncyclic group  over an integral domain  . It is proved that if  is not a field, then there exists a fully invariant ideal  of  such  is torsion-free but not projective as an  -module. In other words, there exists a pure nonprojective variety of group representations over  .
References:
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- A. N. Krasil'nikov, On additive groups of free objects in varieties of integral group representations, Commun. Algebra 23 (1995), 1231--1238. MR 95k:16036
- [M]
- W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), 259--280.
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- H. Neumann, Varieties of Groups, Springer, Berlin, 1967. MR 35:6734
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- B. I. Plotkin, Varieties of group representations, Uspekhi Mat. Nauk 32 (1977), no. 5, 3--68; English transl, Russian Math. Surveys 32 (1977), no. 5, 1--72. MR 57:9849
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- B. I. Plotkin and S. M. Vovsi, Varieties of Group Representations: General Theory, Connections and Applications, Zinatne, Riga, 1983 (Russian). MR 86e:20001
- [S]
- A. Storozhev, On abelian subgroups of relatively free groups, Commun. Algebra 22 (1994), 2677--2701. MR 95d:20066
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- S. M. Vovsi, Topics in Varieties of Group Representations, London Math. Soc. Lecture Notes, vol. 163, Cambr. Univ. Press, Cambridge, 1991. MR 93i:20015
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- S. M. Vovsi, On the semigroups of fully invariant ideals of the free group algebra and the free associative algebra, Proc. Amer. Math. Soc. 119 (1993), 1029--1037. MR 94a:16050
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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:
10.1090/S0002-9939-96-03502-2
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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