On a theorem of Brickman-Fillmore
Abstract: Let be a finite dimensional vector space over an arbitrary field. We show that if and if and are pairwise commuting linear transformations on such that every subspace invariant for both and is also invariant for , then is a polynomial in and . (Brickman and Fillmore proved that if then this statement is true for any finite dimensional vector space .) An example shows that this is not true for .