Geodesic
Algebras with the Same (Algebraic) Geometry
Informatics and Automation, 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. 
@article{TRSPY_2003_242_a13,
     author = {B. I. Plotkin},
     title = {Algebras with the {Same} {(Algebraic)} {Geometry}},
     journal = {Informatics and Automation},
     pages = {176--207},
     publisher = {mathdoc},
     volume = {242},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2003_242_a13/}
}
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B. I. Plotkin. Algebras with the Same (Algebraic) Geometry. Informatics and Automation, Mathematical logic and algebra, Tome 242 (2003), pp. 176-207. http://geodesic.mathdoc.fr/item/TRSPY_2003_242_a13/