EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 56(70), pp. 34--40 (1994)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home

EMIS Home

 		 

Graphical compositions and weak congruences

Miroslav Plo\v s\v cica

Mathematical Institute, Slovak Academy of Sciences, Gre\v sákova 6, 04001 Ko\v sice, Slovakia

Abstract: Graphical compositions of equivalences were introduced (independently) by B. Jónsson and H. Werner in order to determine whether a subset of Eq$(X)$ (the set of all equivalences on the set $X$) is the set of all congruences of some algebra defined on $X$. Namely, a complete sublattice $L$ of Eq$(X)$ is the congruence lattice of some algebra defined on $X$ if and only if $L$ is closed under all graphical compositions. We generalize this result and prove that a similar characterization is possible for weak congruences (i.e., symmetric and transitive compatible relations).

Classification (MSC2000): 03A30, 08A40

Full text of the article:

Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition