Seven Lectures on the Universal Algebraic Geometry

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.

87 pages, uses cd.tex

References in corpus (2)

• Algebras with the same (algebraic) geometry
• Algebraic Logic, Varieties of Algebras and Algebraic Varieties

Cited by in corpus (16)

• Algebras with the same (algebraic) geometry
• Automorphisms of the endomorphism semigroup of a free commutative algebra
• On automorphisms of categories of free algebras of some varieties
• Action Type Geometrical Equivalence of Representations of Groups
• Automorphisms of the semigroup of all endomorphisms of free algebras
• Automorphism groups of endomorphism semigroups of free periodic groups
• Geometrical equivalence, geometrical similarity and geometrical compatibility of algebras
• On logically-geometric types of algebras
• On first order rigidity for linear groups
• Prime types and geometric completeness
• Some remarks on autoequivalences of categories
• A Problem of B. Plotkin for S-Acts: Automorphisms of Categories of Free S-Acts
• Algebraic logic and logically-geometric types in varieties of algebras
• Automorphisms of Categories of Free Modules, Free Semimodules, and Free Lie Modules
• Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
• Lectures notes in universal algebraic geometry