Geodesic
Geometric and conditional geometric equivalences of algebras
Algebra i logika, Tome 51 (2012) no. 6, pp. 766-771.

Voir la notice de l'article provenant de la source Math-Net.Ru

The basis for classifying universal algebras is conventionally formed by one or other type of equivalence relations between the algebras, such as isomorphism, elementary equivalence, equivalence of algebras in other logical languages, geometric equivalence, and so on. Of crucial importance in this event are results that reduce one of such equivalences to another. The most important example (enjoying multiple applications) is the theorem stating that every two algebras are elementarily equivalent iff their ultrapowers with respect to some ultrafilters are isomorphic. Similar results are established for different equivalences of algebras relevant to algebraic geometry of universal algebras.
Keywords: geometrically equivalent algebras, conditionally geometrically equivalent algebras, syntactically implicitly equivalent algebras, $\infty$-quasiequational theory of algebras. 
@article{AL_2012_51_6_a4,
     author = {A. G. Pinus},
     title = {Geometric and conditional geometric equivalences of algebras},
     journal = {Algebra i logika},
     pages = {766--771},
     publisher = {mathdoc},
     volume = {51},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2012_51_6_a4/}
}
TY  - JOUR
AU  - A. G. Pinus
TI  - Geometric and conditional geometric equivalences of algebras
JO  - Algebra i logika
PY  - 2012
SP  - 766
EP  - 771
VL  - 51
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2012_51_6_a4/
LA  - ru
ID  - AL_2012_51_6_a4
ER  - 
%0 Journal Article
%A A. G. Pinus
%T Geometric and conditional geometric equivalences of algebras
%J Algebra i logika
%D 2012
%P 766-771
%V 51
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2012_51_6_a4/
%G ru
%F AL_2012_51_6_a4
A. G. Pinus. Geometric and conditional geometric equivalences of algebras. Algebra i logika, Tome 51 (2012) no. 6, pp. 766-771. http://geodesic.mathdoc.fr/item/AL_2012_51_6_a4/

[1] G. Keisler, Ch. Chen, Teoriya modelei, Mir, M., 1977 | MR

[2] B. I. Plotkin, “Nekotorye ponyatiya algebraicheskoi geometrii v universalnoi algebre”, Algebra i analiz, 9:4 (1997), 224–248 | MR | Zbl

[3] B. Plotkin, “Some results and problems related to universal algebraic geometry”, Int. J. Algebra Comput., 17:5/6 (2007), 1133–1164 | DOI | MR | Zbl

[4] G. Baumslag, A. Myasnikov, V. Remeslennikov, “Algebraic geometry over groups. I: Algebraic sets and ideal theory”, J. Algebra, 219:1 (1999), 16–79 | DOI | MR | Zbl

[5] E. Daniyarova, A. Myasnikov, V. Remeslennikov, “Unification theorems in algebraic geometry”, Aspects of infinite groups, A Festschrift in honor of A. Gaglione, Papers of the conf. in honour of A.Gaglione's 60th birthday (Fairfield, USA, March 2007), Algebra Discr. Math. (Hackensack), 1, eds. B. Fine et al., World Sci., Hackensack, NJ, 2008, 80–111 | DOI | MR | Zbl

[6] A. G. Pinus, “Geometricheskie shkaly mnogoobrazii i kvazitozhdestva”, Matem. tr., 12:2 (2009), 160–169 | MR | Zbl

[7] A. G. Pinus, “Novye algebraicheskie invarianty dlya formulnykh podmnozhestv universalnykh algebr”, Algebra i logika, 50:2 (2011), 209–230 | MR | Zbl

[8] A. G. Pinus, Boolean constructions in universal algebra, Kluwer Acad. Publ., Dordrecht–Boston–London, 1993 | MR | Zbl

[9] A. G. Pinus, “Neyavno ekvivalentnye universalnye algebry”, Sib. matem. zh., 53:5 (2012), 1077–1090 | Zbl