Geodesic
Combining solutions for systems equations in semigroups with finite ideal
Algebra i logika, Tome 55 (2016) no. 1, pp. 87-105.

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

A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is again an algebraic set. We find necessary and sufficient conditions for a semigroup with a finite minimal two-sided ideal (in particular, a finite semigroup) to be an equational domain.
Keywords: semigroups, systems of equations.
Mots-clés : equational domains 
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A. N. Shevlyakov. Combining solutions for systems equations in semigroups with finite ideal. Algebra i logika, Tome 55 (2016) no. 1, pp. 87-105. http://geodesic.mathdoc.fr/item/AL_2016_55_1_a5/

[1] 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. (Fairfield, USA, March 2007 in honour of A. Gaglione's 60th birthday), Algebra Discr. Math. (Hackensack), 1, eds. B. Fine et al., World Sci., Hackensack, NJ, 2008, 80–111 | MR | Zbl

[2] E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad algebraicheskimi sistemami. II. Osnovaniya”, Fundam. prikl. matem., 17:1 (2011/2012), 65–106 | MR

[3] E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad algebraicheskimi sistemami. IV. Ekvatsionalnye oblasti i ko-oblasti”, Algebra i logika, 49:6 (2010), 715–756 | MR

[4] A. N. Shevlyakov, “Ob ob'edinenii reshenii sistem uravnenii v inversnykh polugruppakh”, Vestnik Omskogo un-ta, 2013, no. 4(70), 63–66

[5] A. N. Shevlyakov, “Ob ob'edinenii reshenii sistem uravnenii v kliffordovykh polugruppakh”, Vestnik Omskogo un-ta, 2014, no. 3(73), 18–21

[6] A. N. Shevlyakov, “Ob ob'edinenii reshenii sistem uravnenii v konechnykh prostykh polugruppakh”, Algebra i logika, 53:1 (2014), 109–129 | MR | Zbl

[7] A. Shevlyakov, On disjunctions of equations over semigroups, arXiv: 1305.6842