Rates of growth of p.i. algebras

Berele, Allan

doi:10.1090/S0002-9939-1994-1204370-3

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)

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Rates of growth of p.i. algebras
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by Allan Berele PDF

Proc. Amer. Math. Soc. 120 (1994), 1047-1048 Request permission

Abstract:

Let $A$ be any p.i. algebra in characteristic zero. Then the ${\text {GK}}$-dimension of finitely generated subalgebras is linearly bounded in the number of generators.

References

Allan Berele, Homogeneous polynomial identities, Israel J. Math. 42 (1982), no. 3, 258–272. MR 687131, DOI 10.1007/BF02802727
Allan Berele, Generic verbally prime PI-algebras and their GK-dimensions, Comm. Algebra 21 (1993), no. 5, 1487–1504. MR 1213968, DOI 10.1080/00927879308824632
Allan Berele, Magnum P.I, Israel J. Math. 51 (1985), no. 1-2, 13–19. MR 804472, DOI 10.1007/BF02772954

Varieties and

graded algebras