Pseudocomplemented directoids

Ivan Chajda

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 4, page 533-539
  • ISSN: 0010-2628

Abstract

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Directoids as a generalization of semilattices were introduced by J. Ježek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.

How to cite

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Chajda, Ivan. "Pseudocomplemented directoids." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 533-539. <http://eudml.org/doc/250446>.

@article{Chajda2008,
abstract = {Directoids as a generalization of semilattices were introduced by J. Ježek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.},
author = {Chajda, Ivan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {commutative directoid; $\lambda $-lattice; pseudocomplement; boolean elements; commutative directoid; -lattice; pseudocomplement; Boolean elements},
language = {eng},
number = {4},
pages = {533-539},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Pseudocomplemented directoids},
url = {http://eudml.org/doc/250446},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Chajda, Ivan
TI - Pseudocomplemented directoids
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 533
EP - 539
AB - Directoids as a generalization of semilattices were introduced by J. Ježek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras.
LA - eng
KW - commutative directoid; $\lambda $-lattice; pseudocomplement; boolean elements; commutative directoid; -lattice; pseudocomplement; Boolean elements
UR - http://eudml.org/doc/250446
ER -

References

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  1. Chajda I., Halaš R., Kühr J., Semilattice Structures, Heldermann Verlag, Lemgo (Germany), 2007, ISBN 978-3-88538-230-0. MR2326262
  2. Frink O., Pseudo-complemented semi-lattices, Duke Math. J. 29 (1962), 505-514. (1962) MR0140449
  3. Ježek J., Quackenbush R., 10.1007/BF01190253, Algebra Universalis 27 (1990), 49-69. (1990) MR1025835DOI10.1007/BF01190253
  4. Jones G.T., Pseudo-complemented semi-lattices, Ph.D. Thesis, Univ. of California, Los Angeles, 1972. 
  5. Snášel V., λ -lattices, Math. Bohem. 122 (1997), 267-272. (1997) MR1600648

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