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

TL;DR

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

Contribution

It provides a complete description of the central polynomial T-space for these algebras, a novel result in the theory of polynomial identities.

Findings

Describes the T-space of central polynomials for the algebras.

Applies to fields of characteristic p ≠ 2.

Covers both unitary and nonunitary cases.

Abstract

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