Algebraic geometry over algebraic structures II: Foundations

TL;DR

This paper develops foundational aspects of algebraic geometry over general algebraic structures, introducing key theorems that unify various descriptions of coordinate algebras.

Contribution

It extends algebraic geometry to arbitrary algebraic structures and proves Unification Theorems linking different characterizations of coordinate algebras.

Findings

Introduction of algebraic geometry concepts over arbitrary structures

Proof of Unification Theorems for coordinate algebras

Unified description of coordinate algebras

Abstract

In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.