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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board Member: Blackburn, Simon R. / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Schäge, Sven / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Online
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1869-6104
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On irreducible algebraic sets over linearly ordered semilattices

Artem N. Shevlyakov
  • Sobolev Institute of Mathematics, Pevtsova st. 13, 644099 Omsk, Russia; and Omsk State Technical University, pr. Mira, 11, 644050 Omsk, Russian Federation
  • :
Published Online: 2016-10-11 | DOI: https://doi.org/10.1515/gcc-2016-0014

Abstract

Equations over linearly ordered semilattices are studied. For any equation t(X)=s(X) we find irreducible components of its solution set and compute the average number of irreducible components of all equations in n variables.

Keywords: Semilattice; equation; irreducible algebraic sets

MSC 2010: 06A12


Received: 2016-01-25

Published Online: 2016-10-11

Published in Print: 2016-11-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 14-01-00068

Funding Source: Russian Science Foundation

Award identifier / Grant number: 14-11-00085

The author was supported by Russian Foundation for Basic Research (Grant 14-01-00068, results of Section 4) and Russian Science Foundation (Grant 14-11-00085, results of Section 5).


Citation Information: Groups Complexity Cryptology. Volume 8, Issue 2, Pages 187–195, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2016-0014, October 2016

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