Abstract: It was proved by Giambruno-Segal and Chang that the double Capelli polynomial of total degree 4n is a polynomial identity for Mn(F). (Here, F is a field and Mn(F) is the algebra of n x n matrices over F.) Using a strengthened version of this result obtained by Domokos, we show that the double Capelli polynomial of total degree 4n-2 is a polynomial identity for any proper F-subalgebra of Mn(F). Subsequently, we present a similar result for nonsplit extensions of full matrix algebras.

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