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Groups Complexity Cryptology

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On irreducible algebraic sets over linearly ordered semilattices

Artem N. Shevlyakov
  • Corresponding author
  • Sobolev Institute of Mathematics, Pevtsova st. 13, 644099 Omsk, Russia; and Omsk State Technical University, pr. Mira, 11, 644050 Omsk, Russian Federation
  • Email:
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

References

  • [1]

    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.

  • [2]

    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.

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, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2016-0014. Export Citation

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