The Mikheev identity in right Hom-alternative algebras

TL;DR

This paper demonstrates a Hom-type generalization of the Mikheev identity in right Hom-alternative algebras and explores conditions under which these algebras are actually Hom-alternative.

Contribution

It introduces a Hom-type Mikheev identity and establishes criteria for right Hom-alternative algebras to be Hom-alternative.

Findings

Hom-type Mikheev identity holds in multiplicative right Hom-alternative algebras

Injective twisting map with no Hom-nilpotent elements implies the algebra is Hom-alternative

Provides conditions distinguishing Hom-alternative from right Hom-alternative algebras

Abstract

It is shown that in every multiplicative right Hom-alternative algebra, a Hom-type generalization of the Mikheev identity holds. It is then inferred that a multiplicative right Hom-alternative algebra with an injective twisting map and without Hom-nilpotent elements or left zero-divisors must be a Hom-alternative algebra.