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 (2)

• Seven Lectures on the Universal Algebraic Geometry
• Algebraic Logic, Varieties of Algebras and Algebraic Varieties

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