Congruences on semilattices with section antitone involutions

Ivan Chajda

Discussiones Mathematicae - General Algebra and Applications (2010)

  • Volume: 30, Issue: 2, page 207-215
  • ISSN: 1509-9415

Abstract

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We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.

How to cite

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Ivan Chajda. "Congruences on semilattices with section antitone involutions." Discussiones Mathematicae - General Algebra and Applications 30.2 (2010): 207-215. <http://eudml.org/doc/276569>.

@article{IvanChajda2010,
abstract = {We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.},
author = {Ivan Chajda},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {semilattice; section; antitone involution; congruence kernel; filter; congruence distributivity; 3-permutability; join-semilattice},
language = {eng},
number = {2},
pages = {207-215},
title = {Congruences on semilattices with section antitone involutions},
url = {http://eudml.org/doc/276569},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Ivan Chajda
TI - Congruences on semilattices with section antitone involutions
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2010
VL - 30
IS - 2
SP - 207
EP - 215
AB - We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
LA - eng
KW - semilattice; section; antitone involution; congruence kernel; filter; congruence distributivity; 3-permutability; join-semilattice
UR - http://eudml.org/doc/276569
ER -

References

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  1. [1] J.C. Abbott, Semi-boolean algebras, Matem. Vestnik 4 (1967), 177-198. Zbl0153.02704
  2. [2] J.C. Abbott, Orthoimplication algebras, Studia Logica 35 (1976), 173-177. doi: 10.1007/BF02120879 Zbl0331.02036
  3. [3] I. Chajda, Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carol. 44 (2003), 577-585. Zbl1101.06003
  4. [4] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag (Lemgo, Germany), 220pp., 2003, ISBN 3-88538-226-1. Zbl1014.08001
  5. [5] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 228pp., 2007, ISBN 978-3-88538-230-0. 
  6. [6] I. Chajda, R. Halaš and J. Kühr, Implication in MV-algebras, Algebra Universalis 53 (2005), 377-382. doi: 10.1007/s00012-004-1862-4 Zbl1097.06011

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