, Volume 103, Issue 1, pp 17-28

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 1J 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.

Partially supported by NSF grant DMS 9303230.
Partially supported by NSF grant DMS 9101488.