On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields

TL;DR

This paper establishes a basis for the graded identities of matrix algebras over infinite fields with elementary gradings, extending understanding of algebraic identities in positive characteristic.

Contribution

It provides a complete basis for G-graded identities of matrix algebras with elementary gradings over infinite fields of positive characteristic.

Findings

Identifies a basis for G-graded identities in the specified setting

Extends known results to fields of positive characteristic

Clarifies the structure of graded identities in matrix algebras

Abstract

We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$.