Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1040,
author = {Ivan Chajda and Helmut L\"anger},
title = {Congruence classes in Brouwerian semilattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {21},
year = {2001},
pages = {229-237},
zbl = {1016.08003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1040}
}
Ivan Chajda; Helmut Länger. Congruence classes in Brouwerian semilattices. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 229-237. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1040/
[000] [1] J. Duda, Arithmeticity at 0, Czechoslovak Math. J. 37 (1987), 197-206. | Zbl 0627.08003
[001] [2] K. Fichtner, Eine Bemerkung über Mannigfaltigkeiten universeller Algebren mit Idealen, Monatsb. Deutsch. Akad. Wiss. Berlin 12 (1970), 21-25. | Zbl 0198.33601
[002] [3] P. Köhler, Brouwerian semilattices: the lattice of total subalgebras, Banach Center Publ. 9 (1982), 47-56.
[003] [4] W.C. Nemitz, Implicative semi-lattices, Trans. Amer. Math. Soc. 117 (1965), 128-142. | Zbl 0128.24804