Seven Lectures on the Universal Algebraic Geometry

TL;DR

This paper explores universal algebraic geometry, extending algebraic geometry concepts to arbitrary algebraic varieties by examining the interplay between algebra, logic, and geometry within these structures.

Contribution

It introduces a unified framework for universal algebraic geometry applicable to various algebraic varieties, bridging algebraic, logical, and geometric perspectives.

Findings

Defines universal algebraic geometry for arbitrary algebraic varieties

Establishes connections between algebra, logic, and geometry

Provides foundational concepts for further research in the field

Abstract

Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in algebras from a given variety of algebras.