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) 2018: 0.29

Print + Online
See all formats and pricing
More options …
Volume 64, Issue 3


Weak subgroupoid lattices

Alfonz Haviar / Miroslav Haviar
Published Online: 2014-07-05 | DOI: https://doi.org/10.2478/s12175-014-0232-8


The aim of the paper is a characterization of the lattice of all weak subgroupoids of a partial groupoid. It also extends to arbitrary finite algebras Pióro’s result saying that the weak subgroupoid lattice of a finite commutative groupoid G in which g·h ≠ g (for all g, h ∈ G) uniquely determines its subgroupoid lattice.

MSC: Primary 08A55; Secondary 06B15

Keywords: weak subalgebra; weak subgroupoid

  • [1] BALCAR, B.— ŠTĚPÁNEK, P.: Set Theory, Academia, Praha, 1986 (Czech). Google Scholar

  • [2] BARTOL, W.: Weak subalgebra lattices, Comment. Math. Univ. Carolin. 31 (1990), 405–410. Google Scholar

  • [3] HALL, P.: On representatives of subsets, J. Lond. Math. Soc. (2) 10 (1935), 26–30. Google Scholar

  • [4] PIÓRO, K.: On a strong property of the weak subalgebra lattice, Algebra Universalis 40 (1998), 477–495. http://dx.doi.org/10.1007/s000120050096CrossrefGoogle Scholar

  • [5] PIÓRO, K.: On connections between hypergraphs and algebras, Arch. Math. (Brno) 36 (2000), 45–60. Google Scholar

  • [6] PIÓRO, K.: The weak subalgebra lattice of a unary partial algebra of a given infinite unary type, Math. Slovaca 51 (2001), 295–320. Google Scholar

  • [7] PIÓRO, K.: On subgroupoid lattices of some finite groupoid, Acta Math. Univ. Comenian. (N.S.) LXXII (2003), 147–158. Google Scholar

About the article

Published Online: 2014-07-05

Published in Print: 2014-06-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 3, Pages 665–674, ISSN (Online) 1337-2211, DOI: https://doi.org/10.2478/s12175-014-0232-8.

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