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Algebra Logika, 2016, Volume 55, Number 1, Pages 87–105 (Mi al731)  

Combining solutions for systems equations in semigroups with finite ideal

A. N. Shevlyakovab

a Omsk State Technical University, pr. Mira 11, Omsk, 644050 Russia
b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099 Russia

Abstract: 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, equational domains, systems of equations.

Funding Agency Grant Number
Russian Science Foundation 14-11-00085
Russian Foundation for Basic Research 14-01-00068
The work is supported by Russian Science Foundation, project 14-11-00085 (Section 5), and by RFBR, project No. 14-01-00068 (Sections 3 and 4).


DOI: https://doi.org/10.17377/alglog.2016.55.106

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English version:
Algebra and Logic, 2016, 55:1, 58–71

Bibliographic databases:

UDC: 512.53
Received: 27.03.2015
Revised: 10.07.2015

Citation: A. N. Shevlyakov, “Combining solutions for systems equations in semigroups with finite ideal”, Algebra Logika, 55:1 (2016), 87–105; Algebra and Logic, 55:1 (2016), 58–71

Citation in format AMSBIB
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