Algebras with the Same (Algebraic) Geometry
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 176-207.

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Some basic notions of classical algebraic geometry can be defined on 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.
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B. I. Plotkin. Algebras with the Same (Algebraic) Geometry. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 176-207. http://geodesic.mathdoc.fr/item/TM_2003_242_a13/

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