# 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

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topIvan 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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- [5] I. Chajda and R. Radeleczki, Semilattices with sectionally antitone bijections, Novi Sad J. Math. 35 (2005), 93-101. Zbl1274.06012
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- [7] J. Hagemann and A. Mitschke, On n-permutable congruences, Algebra Universalis 3 (1973), 8-12.
- [8] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69. Zbl0699.08002
- [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] S. Radeleczki, The congruence lattice of implication algebras, Math. Pannonica 3 (1992), 115-123.
- [11] V. Snášel, λ-lattices, Math. Bohemica 122 (1997), 267-272.

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