Geometrical equivalence, geometrical similarity and geometrical compatibility of algebras

TL;DR

This paper investigates conditions under which algebras within a certain variety share identical algebraic geometries, focusing on concepts of geometrical equivalence, similarity, and compatibility.

Contribution

It introduces and analyzes conditions related to geometrical equivalence, similarity, and compatibility that determine when algebras have coinciding algebraic geometries.

Findings

Identifies conditions for algebraic geometry coincidence

Defines and explores geometrical equivalence, similarity, and compatibility

Provides theoretical insights into algebraic geometry relationships

Abstract

In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.