Geodesic
Implicit algebraic geometry of universal algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 40-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the notion of an implicit operation on universal algebras, we redefine basic notions of the algebraic geometry of universal algebras. The results obtained for the implicit algebraic geometry imply (as special cases) the known results on the conditional geometrical and algebraic geometrical comparability of algebras.
Mots-clés : algebraic
Keywords: conditional algebraic geometries of universal algebras, implicit operations, varieties, pseudovarieties. 
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A. G. Pinus. Implicit algebraic geometry of universal algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2012), pp. 40-45. http://geodesic.mathdoc.fr/item/IVM_2012_5_a3/

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

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

[3] Baumslag G., Myasnikov A., Remeslennikov V., “Algebraic geometry over groups. I. Algebraic sets and ideal theory”, J. Algebra, 219:2 (1999), 16–77 | DOI | MR

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

[5] Bludov V. V., Gusev B. V., “Geometricheskaya ekvivalentnost grupp”, Tr. in-ta matem. i mekhaniki Uro RAN, 13, no. 1, 2007, 57–78 | MR

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

[7] Pinus A. G., Uslovnye termy i ikh prilozheniya v algebre i teorii vychislenii, Izd-vo NGTU, Novosibirsk, 2002

[8] Pinus A. G., “Uslovnye termy i ikh prilozheniya v algebre i teorii vychislenii”, UMN, 56:4 (2001), 35–72 | MR | Zbl

[9] Pinus A. G., “O neyavnykh uslovnykh operatsiyakh na psevdouniversalnykh klassakh”, Fundament. i prikl. matem., 10:4 (2004), 171–182 | MR | Zbl

[10] Pinus A. G., “Pozitivno-uslovnye mnogoobraziya i neyavnye operatsii na nikh”, Sib. matem. zhurn., 47:2 (2006), 372–382 | MR | Zbl