Geodesic
Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 75-100

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This paper belongs to our series of works on algebraic geometry over arbitrary algebraic structures. In this one, there will be investigated seven equivalences (namely: geometrical, universal geometrical, quasi-equational, universal, elementary, and combinations thereof) in specific classes of algebraic structures (equationally Noetherian, $\mathrm{q}_\omega$-compact, $\mathrm{u}_\omega$-compact, equational domains, equational co-domains, etc.). The main questions are the following: (1) Which equivalences coincide inside a given class $\mathbf K$, which do not? (2) With respect to which equivalences a given class $\mathbf K$ is invariant, with respect to which it is not? 
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     author = {E. Yu. Daniyarova and A. G. Myasnikov and V. N. Remeslennikov},
     title = {Algebraic geometry over algebraic structures. {VIII.} {Geometric} equivalences and special classes of algebraic structures},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {75--100},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a5/}
}
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E. Yu. Daniyarova; A. G. Myasnikov; V. N. Remeslennikov. Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 4, pp. 75-100. http://geodesic.mathdoc.fr/item/FPM_2019_22_4_a5/