Algebraic geometry over algebraic structures II: Foundations

2010/02/18 by Evelina Daniyarova, Daniyarova, Evelina, Alexei Myasnikov +3
Mathematics · #03C99 #08A99 #14A99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #math.AG #math.LO #msc:03C99 #msc:08A99 #msc:14A99

paper · pdf · doi:10.48550/arxiv.1002.3562

55 pages

arxiv created 2011/02/02 · arxiv updated 2011/02/03

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.

Related

• Unification theorems in algebraic geometry
• Algebras with the same (algebraic) geometry
• Seven Lectures on the Universal Algebraic Geometry
• Algebraic Logic, Varieties of Algebras and Algebraic Varieties
• Algebraic logic and logical geometry in arbitrary varieties of algebras