A note in algebras with Laurent polynomial identity

TL;DR

This paper explores algebraic structures with Laurent polynomial identities, extending existing results and proposing a new version of Hartley's conjecture related to these identities.

Contribution

It introduces new results on algebras with Laurent polynomial identities and presents a revised version of Hartley's conjecture involving these identities.

Findings

Extended results on algebras with Laurent polynomial identities

Proposed a new version of Hartley's conjecture

Provided insights into the structure of units in such algebras

Abstract

In this article, we extend some results about algebra $A$ with the group of units $U(A)$ having a special polynomial identity, Laurent polynomial. And we present a new version of B. Hartley Conjecture with these identities.