The standard identity in algebra \(M_{n,n}(E)\) (Q6597466)

The Amitsur-Levitzki Theorem (1950) states that the algebra of \(n\times n\) matrices over a field satisfies a certain identity of degree \(2n\) and this is the smallest possible degree.\N\NIn this paper, the author shows an analogous version of the Amitsur-Levitzki theorem applied to the algebra \(M_n(E),\) where \(E\) is the Grassmann algebra over a field of odd characteristic \(p\). In this case (see Theorem 5 and Theorem 7) the minimal degree of a polynomial identity is \(2np.\)\N\NFurther results are presented in Section 4 for the case of non-square matrices.