Geodesic
Algebraic geometry over algebraic structures. VI. Geometric equivalence
Algebra i logika, Tome 56 (2017) no. 4, pp. 421-442

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The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures $\mathcal A$ and $\mathcal B$ of a language $\mathrm L$, the classification problems for algebraic sets over $\mathcal A$ and $\mathcal B$ are equivalent. We establish a connection between geometrical equivalence and quasi-equational equivalence.
Keywords: universal algebraic geometry, geometrical equivalence, prevariety, quasivariety.
Mots-clés : algebraic structure 
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     title = {Algebraic geometry over algebraic {structures.~VI.} {Geometric} equivalence},
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     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_4_a2/}
}
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E. Yu. Daniyarova; A. G. Myasnikov; V. N. Remeslennikov. Algebraic geometry over algebraic structures. VI. Geometric equivalence. Algebra i logika, Tome 56 (2017) no. 4, pp. 421-442. http://geodesic.mathdoc.fr/item/AL_2017_56_4_a2/