CODIMENSIONS OF PRODUCTS AND OF INTERSECTIONS OF VERBALLY PRIME T-IDEALS

By Kemer's theory [9], T ideals J(1) boolean AND ...boolean AND J(r) a nd J(1) .. J(r), where each J(i) is verbally prime, are of fundamental importance in the theory of P.I. algebras. We calculate, approximatel y and asymptotically, the codimensions of such T-ideals, thereby exten ding the corresponding results about matrix algebras. In all such case s, the exponential growth of the codimensions is calculated; in partic ular, it is always an integer.