# Congruences on semilattices with section antitone involutions

Discussiones Mathematicae - General Algebra and Applications (2010)

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

## Access Full Article

top## Abstract

top## How to cite

topIvan 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

top- [1] J.C. Abbott, Semi-boolean algebras, Matem. Vestnik 4 (1967), 177-198. Zbl0153.02704
- [2] J.C. Abbott, Orthoimplication algebras, Studia Logica 35 (1976), 173-177. doi: 10.1007/BF02120879 Zbl0331.02036
- [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] 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] I. Chajda, R. Halaš and J. Kühr, Semilattice Structures, Heldermann Verlag (Lemgo, Germany), 228pp., 2007, ISBN 978-3-88538-230-0.
- [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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.