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Rates of growth of p.i. algebras


Author: Allan Berele
Journal: Proc. Amer. Math. Soc. 120 (1994), 1047-1048
MSC: Primary 16R99; Secondary 16P90
DOI: https://doi.org/10.1090/S0002-9939-1994-1204370-3
MathSciNet review: 1204370
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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 [Enhancements On Off] (What's this?)

  • [1] A. Berele, Homogeneous polynomial identities, Israel J. Math. 42 (1982), 258-272. MR 687131 (84b:16018)
  • [2] -, Generic verbally prime algebras and the $ GK$-dimensions, Comm. Algebra 21 (1993), 1487-1504. MR 1213968 (94f:16038)
  • [3] -, Magnum p.i., Israel J. Math. 51 (1985), 13-19. MR 804472 (87b:16019)
  • [4] A. R. Kemer, Varieties and $ {Z_2}$-graded algebras, Math. USSR-Izv. 25 (1985), 359-374.

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DOI: https://doi.org/10.1090/S0002-9939-1994-1204370-3
Article copyright: © Copyright 1994 American Mathematical Society

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