Two-Generated Commutative Subalgebras of Mn(F) Original Research Article

For two commuting matrices A, B set membership, variant Mn (K), K a field, it has been known that dimKK[A, B] ≤ n. We show here that dimK CentMn(K)(A, B) ≥ n and that equality for one implies equality for the other. We also give both a module theoretic and a geometric characterization of those algebras for which equality is obtained. Furthermore, we present a new proof of a result of Gerstenhaber.