2004/05/06 by Daniel Birmajer, Birmajer, Daniel
Computer Science · Mathematics · #15A24 #16R10 #Advanced Topics in Algebra #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.RA #msc:15A24 #msc:16R10
paper · pdf · doi:10.48550/arxiv.math/0405102
6 pages, accepted in the Proceedings of the American Mathematical Society
arxiv created 2004/05/06 · openalex publication_date 2004/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It 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.