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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the semigroups of fully invariant ideals of the free group algebra and the free associative algebra
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by Samuel M. Vovsi PDF
Proc. Amer. Math. Soc. 119 (1993), 1029-1037 Request permission

Abstract:

Let $R$ be an integral domain, $K$ its field of fractions, $F$ a free group. Let $I$ and $J$ be fully invariant (=verbal) ideals of the group algebra $KF$. We prove that over certain domains the equality $IJ \cap RF = (I \cap RF) \times (J \cap RF)$ 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
  • © Copyright 1993 American Mathematical Society
  • 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