Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 64, Issue 4

Issues

Characterizations of strong Morita equivalence for ordered semigroups with local units

Lauri Tart
  • Institute of Mathematics Faculty of Mathematics and Computer Science, University of Tartu, J. Liivi 2, 50090, Tartu, Estonia
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-09-07 | DOI: https://doi.org/10.2478/s12175-014-0240-8

Abstract

We prove that partially ordered semigroups S and T with local units are strongly Morita equivalent if and only if there exists a surjective strict local isomorphism to T from a factorizable Rees matrix posemigroup over S. We also provide two similar descriptions which use Cauchy completions and Morita posemigroups instead.

MSC: Primary 06F05; Secondary 20M10

Keywords: ordered semigroup; Morita equivalence; Rees matrix cover

  • [1] BULMAN-FLEMING, S.: Flatness properties of S-posets: an overview. In: Proceedings of the International Conference on Semigroups, Acts and Categories with Applications to Graphs, Tartu, 2007 (V. Laan, S. Bulman-Fleming, R. Kaschek, eds.), Estonian Mathematical Society, Tartu, 2008, pp. 28–40. Google Scholar

  • [2] HOWIE, J. M.: Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995. Google Scholar

  • [3] KELLY, G. M.: Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Note Ser. 64, Cambridge Univ. Press, New York, 1982. Google Scholar

  • [4] LAAN, V.: Context equivalence of semigroups, Period. Math. Hungar. 60 (2010), 81–94. http://dx.doi.org/10.1007/s10998-010-1081-zCrossrefGoogle Scholar

  • [5] LAAN, V.— MÁRKI, L.: Morita invariants for semigroups with local units, Monatsh. Math. 166 (2012), 441–451. http://dx.doi.org/10.1007/s00605-010-0279-8Web of ScienceCrossrefGoogle Scholar

  • [6] LAAN, V.— MÁRKI, L.: Strong Morita equivalence of semigroups with local units, J. Pure Appl. Algebra 215 (2011), 2538–2546. http://dx.doi.org/10.1016/j.jpaa.2011.02.017Web of ScienceCrossrefGoogle Scholar

  • [7] LAWSON, M. V.: Morita equivalence of semigroups with local units, J. Pure Appl. Algebra 215 (2011), 455–470. http://dx.doi.org/10.1016/j.jpaa.2010.04.030CrossrefWeb of ScienceGoogle Scholar

  • [8] MCALISTER, D. B.: Regular Rees matrix semigroups and regular Dubreil-Jacotin semigroups, J. Aust. Math. Soc. Ser. A 31 (1981), 325–336. http://dx.doi.org/10.1017/S1446788700019467CrossrefGoogle Scholar

  • [9] TALWAR, S.: Morita equivalence for semigroups, J. Aust. Math. Soc. Ser. A 59 (1995), 81–111. http://dx.doi.org/10.1017/S1446788700038489CrossrefGoogle Scholar

  • [10] TALWAR, S.: Strong Morita equivalence and a generalisation of the Rees theorem, J. Algebra 181 (1996), 371–394. http://dx.doi.org/10.1006/jabr.1996.0125CrossrefGoogle Scholar

  • [11] TART, L.: Conditions for strong Morita equivalence of partially ordered semigroups, Cent. Eur. J. Math. 9 (2011), 1100–1113. http://dx.doi.org/10.2478/s11533-011-0053-8CrossrefGoogle Scholar

  • [12] TART, L.: Strong Morita equivalence for ordered semigroups with local units, Period. Math. Hungar. 65 (2012), 29–43. http://dx.doi.org/10.1007/s10998-012-7140-xCrossrefGoogle Scholar

  • [13] TART, L.: Subobject Classification and Geometric Morphisms of Partially Ordered Acts, Master Thesis, University of Tartu, 2005. Google Scholar

About the article

Published Online: 2014-09-07

Published in Print: 2014-08-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 4, Pages 789–808, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0240-8.

Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in