The identities and central polynomials of the finite dimensional unitary Grassmann algebras over a finite field

TL;DR

This paper characterizes the identities and central polynomials of finite dimensional unitary Grassmann algebras over finite fields, providing a detailed algebraic description of their polynomial identities.

Contribution

It explicitly describes the T-ideal of identities and T-space of central polynomials for these algebras, advancing understanding of their algebraic structure.

Findings

Explicit description of the T-ideal of identities.

Explicit description of the T-space of central polynomials.

Enhanced understanding of algebraic structure of Grassmann algebras over finite fields.

Abstract

We describe the T-ideal of identities and the T-space of central polynomials for the unitary finite dimensional Grassmann algebra over a finite field.