Polynomial identities of finite prime Universal algebras

TL;DR

This paper proves that finite prime universal algebras over a commutative ring with identical polynomial identities are necessarily isomorphic, establishing a strong link between identities and algebra structure.

Contribution

It demonstrates that polynomial identities uniquely determine finite prime universal algebras up to isomorphism.

Findings

Finite prime $ ext{Ω}$-algebras with the same identities are isomorphic.

Polynomial identities characterize algebra structure in this class.

The result applies over unital commutative rings.

Abstract

We prove that two finite prime $\Omega$-algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.