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Identifying Solutions to Systems of Equations in Semigroups with Finite Ideal

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Algebra and Logic Aims and scope

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.

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Authors and Affiliations

  1. Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    A. N. Shevlyakov

  2. Omsk State Technical University, pr. Mira 11, Omsk, 644050, Russia

    A. N. Shevlyakov

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  1. A. N. Shevlyakov
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Correspondence to A. N. Shevlyakov.

Additional information

(A. N. Shevlyakov) 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).

Translated from Algebra i Logika, Vol. 55, No. 1, pp. 87-105, January-February, 2016.

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Shevlyakov, A.N. Identifying Solutions to Systems of Equations in Semigroups with Finite Ideal. Algebra Logic 55, 58–71 (2016). https://doi.org/10.1007/s10469-016-9376-7

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  • DOI: https://doi.org/10.1007/s10469-016-9376-7

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