ArticleOriginal scientific text
Title
Congruence classes in Brouwerian semilattices
Authors 1, 2
Affiliations
- Palacký University of Olomouc, Department of Algebra and Geometry, Tomkova 40, CZ-77900 Olomouc
- Technische Universität Wien, Institut für Algebra und Computermathematik, Wiedner Hauptstraß e 8-10, A-1040 Wien
Abstract
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.
Keywords
congruence class, Brouwerian semilattice, ideal
Bibliography
- J. Duda, Arithmeticity at 0, Czechoslovak Math. J. 37 (1987), 197-206.
- K. Fichtner, Eine Bemerkung über Mannigfaltigkeiten universeller Algebren mit Idealen, Monatsb. Deutsch. Akad. Wiss. Berlin 12 (1970), 21-25.
- P. Köhler, Brouwerian semilattices: the lattice of total subalgebras, Banach Center Publ. 9 (1982), 47-56.
- W.C. Nemitz, Implicative semi-lattices, Trans. Amer. Math. Soc. 117 (1965), 128-142.
Pages:
229-237
Main language of publication
English
Received
2001-08-14
Accepted
2001-12-12
Published
2001
DOI: 10.7151/dmgaa.1040
Exact and natural sciences