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Codimensions of products and of intersections of verbally primeT-ideals

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Abstract

By Kemer’s theory [9],T idealsJ 1 ∪…∪J r andJ 1 …J r, where eachJ i is verbally prime, are of fundamental importance in the theory of P.I. algebras. We calculate, approximately and asymptotically, the codimensions of suchT-ideals, thereby extending the corresponding results about matrix algebras. In all such cases, the exponential growth of the codimensions is calculated; in particular, it is always an integer.

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Authors and Affiliations

  1. Mathematics Department, DePaul University, 60614, Chicago, IL, USA

    A. Berele

  2. Department of Mathematics, The Pennsylvania State University, 16802, University Park, PA, USA

    A. Regev

Authors
  1. A. Berele
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  2. A. Regev
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Corresponding authors

Correspondence to A. Berele or A. Regev.

Additional information

Partially supported by NSF grant DMS 9303230.

Partially supported by NSF grant DMS 9101488.

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Berele, A., Regev, A. Codimensions of products and of intersections of verbally primeT-ideals. Isr. J. Math. 103, 17–28 (1998). https://doi.org/10.1007/BF02762265

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  • DOI: https://doi.org/10.1007/BF02762265

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