On Dominance and Varieties of Commuting Matrices

摘要: [4]), a question first raised by Goto. In the same section it is shown that algebra generated pair of commuting n x matrices can not have dimension greater than n, and this always be embedded in commutative exactly result derived introducing notion specialization an matrices. The remainder Chapter II contains related results independent interest included mainly for later reference. present paper was originally intended to part "On nilalgebras linear varieties nilpotent matrices, IV" (in preparation), which study continues program determining structure (" nilvarieties "). It there if V nilvariety c all with generic element V, then dim V_? 1/2(n2 c). All l/2(X2-c) are determined associative algebras type we elected call anti-semisimple. These may described