Algebras with the same (algebraic) geometry

Abstract

Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras $\Theta .$ For every algebra $H$ in $\Theta$ one can consider algebraic geometry in $\Theta$ over $H.$ Correspondingly, algebras in $\Theta$ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in $\Theta$ and of geometric relations between them. The main problem considered in the paper is when different $H_1$ and $H_2$ have the same geometry.

52 pages, cd.tex

References in corpus (1)

• Algebraic Logic, Varieties of Algebras and Algebraic Varieties

Cited by in corpus (10)

• The group of automorphisms of the category of free associative algebras
• On automorphisms of categories of free algebras of some varieties
• Action Type Geometrical Equivalence of Representations of Groups
• Geometrical equivalence, geometrical similarity and geometrical compatibility of algebras
• A generalization and a new proof of Plotkin's reduction theorem
• Automorphisms of the category of free Lie algebras
• The group of automorphisms of semigroup End
• Problems in algebra inspired by universal algebraic geometry
• Some remarks on autoequivalences of categories
• Aupomorphisms of the category of the free nilpotent groups of the fixed class of nilpotency