Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

Abstract

The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures \( \mathcal{A} \) and ℬ of a language L, the classification problems for algebraic sets over \( \mathcal{A} \) and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.