The central polynomials of the finite dimensional unitary and nonunitary Grassmann algebras

TL;DR

This paper characterizes the T-space of central polynomials for finite dimensional Grassmann algebras, both unitary and nonunitary, over fields with characteristic not equal to 2, expanding understanding of their algebraic identities.

Contribution

It provides a detailed description of the central polynomials' T-space for finite dimensional Grassmann algebras in characteristic p ≠ 2, including the infinite field case for unitary algebras.

Findings

Describes the T-space of central polynomials for finite dimensional Grassmann algebras.

Extends results to both unitary and nonunitary cases.

Includes the case of infinite fields for unitary Grassmann algebras.

Abstract

We describe the T-space of central polynomials for both the unitary and the nonunitary finite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).