A variant of Rosset's approach to the Amitsur-Levitzki theorem and some $\mathbb{Z}_{2}$-graded identities of $\mathrm{M}_{n}(E)$

Authors: Szilvia Homolya, JEN? SZIGETI

Abstract: In the spirit of Rosset's proof of the Amitsur-Levitzki theorem, we show how the standard identiy (for matrices over a commutative base ring) and the addition of external Grassmann variables can be used to derive a certain $\mathbb{Z}_{2}$-graded polynomial identity of $\mathrm{M}_{n}(E)$.

Keywords: The full matrix algebra over the infinite dimensional Grassmann algebra, the Amitsur-Levitzki theorem on $n\times n$ matrices

Full Text: PDF