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Algebras with the same (algebraic) geometry

B. Plotkin
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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 $H_1$ and $H_2$ have the same geometry.

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B. Plotkin. 2002-10-14. Algebras with the same (algebraic) geometry. https://arxiv.org/abs/math/0210194

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