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 $\mathrm{M}_{n}(E)$.

DOI

10.55730/1300-0098.3237

Keywords

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

First Page

1864

Last Page

1870

Recommended Citation

Homolya, S, & SZIGETI, J (2022). A variant of Rosset's approach to the Amitsur-Levitzki theorem and some $\mathbb{Z}_{2}$-graded identities of $\mathrm{M}_{n}(E)$. Turkish Journal of Mathematics 46 (5): 1864-1870. https://doi.org/10.55730/1300-0098.3237