Commutative directoids with sectionally antitone bijections

Ivan Chajda; Miroslav Kolařík; Sándor Radeleczki

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 1, page 77-89
  • ISSN: 1509-9415

Abstract

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We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.

How to cite

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Ivan Chajda, Miroslav Kolařík, and Sándor Radeleczki. "Commutative directoids with sectionally antitone bijections." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 77-89. <http://eudml.org/doc/276838>.

@article{IvanChajda2008,
abstract = {We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.},
author = {Ivan Chajda, Miroslav Kolařík, Sándor Radeleczki},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {directoid; section antitone bijection; implication algebra; double implication algebra; sectionally antitone bijection},
language = {eng},
number = {1},
pages = {77-89},
title = {Commutative directoids with sectionally antitone bijections},
url = {http://eudml.org/doc/276838},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Ivan Chajda
AU - Miroslav Kolařík
AU - Sándor Radeleczki
TI - Commutative directoids with sectionally antitone bijections
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 1
SP - 77
EP - 89
AB - We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
LA - eng
KW - directoid; section antitone bijection; implication algebra; double implication algebra; sectionally antitone bijection
UR - http://eudml.org/doc/276838
ER -

References

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  1. [1] J.C. Abbott, Semi-Boolean algebras, Matem. Vestnik 4 (1967), 177-198. Zbl0153.02704
  2. [2] I. Chajda, Lattices and semilattices having an antitone bijection in any upper interval, Comment. Math. Univ. Carolinae 44 (2003), 577-585. Zbl1101.06003
  3. [3] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo (Germany), 2003, ISBN 3-88538-226-1. Zbl1014.08001
  4. [4] I. Chajda and M. Kolařík, Directoids with sectionally antitone involutions and skew MV-algebras, Math. Bohemica 132 (2007), 407-422. Zbl1174.06314
  5. [5] I. Chajda and R. Radeleczki, Semilattices with sectionally antitone bijections, Novi Sad J. Math. 35 (2005), 93-101. Zbl1274.06012
  6. [6] B. Csákány, Characterization of regular varieties, Acta Sci. Math. Szeged 31 (1970), 187-189. 
  7. [7] J. Hagemann and A. Mitschke, On n-permutable congruences, Algebra Universalis 3 (1973), 8-12. 
  8. [8] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69. Zbl0699.08002
  9. [9] V.M. Kopytov and Z.I. Dimitrov, On directed groups, Siberian Math. J. 30 (1989), 895-902. (Russian original: Sibirsk. Mat. Zh. 30 (6) (1988), 78-86.) 
  10. [10] S. Radeleczki, The congruence lattice of implication algebras, Math. Pannonica 3 (1992), 115-123. 
  11. [11] V. Snášel, λ-lattices, Math. Bohemica 122 (1997), 267-272. 

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