@MISC{Plotkin09algebraswith, author = {B. Plotkin}, title = {Algebras with the same (algebraic) geometry}, year = {2009} }

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Abstract

Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in Θ and of geometric relations between them. The main problem considered in the paper is when different H1 and H2 have the same geometry.