Relatively pseudocomplemented directoids

Ivan Chajda

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 3, page 349-357
  • ISSN: 0010-2628

Abstract

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The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called p -ideals.

How to cite

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Chajda, Ivan. "Relatively pseudocomplemented directoids." Commentationes Mathematicae Universitatis Carolinae 50.3 (2009): 349-357. <http://eudml.org/doc/33319>.

@article{Chajda2009,
abstract = {The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$-ideals.},
author = {Chajda, Ivan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity; directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity},
language = {eng},
number = {3},
pages = {349-357},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relatively pseudocomplemented directoids},
url = {http://eudml.org/doc/33319},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Chajda, Ivan
TI - Relatively pseudocomplemented directoids
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 3
SP - 349
EP - 357
AB - The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$-ideals.
LA - eng
KW - directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity; directoid; relative pseudocomplementation; filter; congruence distributivity; congruence weak regularity
UR - http://eudml.org/doc/33319
ER -

References

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  1. Chajda I., Pseudocomplemented directoids, Comment. Math. Univ. Carolin. 49 (2008), 533--539. MR2493936
  2. Chajda I., Halaš R., Kühr J., Semilattice Structures, Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0. MR2326262
  3. Ježek J., Quackenbush R., 10.1007/BF01190253, Algebra Universalis 27 (1990), 49--69. MR1025835DOI10.1007/BF01190253
  4. Jones G.T., Pseudo-complemented semi-lattices, Ph.D. Thesis, Univ. of California, Los Angeles, 1972. 
  5. Snášel V., ł a m b d a -lattices, Math. Bohem. 122 (1997), 267--272. MR1600648
  6. Chajda I., Rachůnek J., 10.1007/BF00353659, Order 5 (1989), 407--423. MR1010389DOI10.1007/BF00353659

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