On the semigroups of fully invariant ideals of the free group algebra and the free associative algebra
Author:
Samuel M. Vovsi
Journal:
Proc. Amer. Math. Soc. 119 (1993), 1029-1037
MSC:
Primary 16S34; Secondary 20C07
DOI:
https://doi.org/10.1090/S0002-9939-1993-1154250-6
MathSciNet review:
1154250
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an integral domain,
its field of fractions,
a free group. Let
and
be fully invariant (=verbal) ideals of the group algebra
. We prove that over certain domains the equality
need not be true. A similar result is valid for fully invariant ideals of the free associative algebra. This implies that the product of pure varieties of group representations over an integral domain need not be pure, that there exist pure nonprojective varieties of group representations and of associative algebras, and also answers some other questions raised in the literature.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1993-1154250-6
Article copyright:
© Copyright 1993
American Mathematical Society