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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

CiteScore 2017: 0.32

SCImago Journal Rank (SJR) 2017: 0.208
Source Normalized Impact per Paper (SNIP) 2017: 0.322

Mathematical Citation Quotient (MCQ) 2017: 0.32

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On irreducible algebraic sets over linearly ordered semilattices

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


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


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    Daniyarova E. Y., Myasnikov A. G. and Remeslennikov V. N., Algebraic geometry over algebraic structures. II: Foundations, J. Math. Sci. 185 (2012), no. 3, 389–416. Google Scholar

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    Ben-Or M., Lower bounds for algebraic computation trees, Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing (STOC’83), ACM, New York (1983), 80–86. Google Scholar

About the article

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.

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