2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71074It was proved by Giambruno-Sehgal and Chang that the double Capelli polynomial of total degree $4n$ is a polynomial identity for the algebra of n by n matrices over a field 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 matrix subalgebra. Subsequently, we present a similar result for nonsplit extensions of full matrix algebras.6 pages, accepted in the Proceedings of the American Mathematical SocietyRings and Algebras16R10; 15A24text