2-GENERATED COMMUTATIVE SUBALGEBRAS OF M(N)(F)

For two commuting matrices A, B is-an-element-of M(n) (K), K a field, it has been known that dim(K) K[A, B] less-than-or-equal-to n. We show here that dim(K) Cent(Mn(K))(A, B) greater-than-or-equal-to n and tha t equality for one implies equality for the other. We also give both a module theoretic and a geometric characterization of those algebras f or which equality is obtained. Furthermore, we present a new proof of a result of Gerstenhaber. (C) 1994 Academic Press, Inc.