On geometrically equivalent S-acts

TL;DR

This paper explores geometric equivalence among S-acts over monoids, providing representation theorems that classify all types of equivalence classes within varieties over groups, enhancing understanding of their structural relationships.

Contribution

It introduces new representation theorems that classify geometrically equivalent S-acts over groups, expanding the theoretical framework of algebraic structures.

Findings

Classification of all types of geometrically equivalent S-acts

Representation theorems for equivalence classes

Enhanced understanding of algebraic structure relationships

Abstract

In this paper, considering the geometric equivalence for algebras of a variety $_{S}A$ of S-acts over a monoid S, we obtain representation theorems describing all types of the equivalence classes of geometrically equivalent S-acts of varieties $_{S}A$ over groups S.