PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 56(70), pp. 3440 (1994) 

Graphical compositions and weak congruencesMiroslav Plo\v s\v cicaMathematical Institute, Slovak Academy of Sciences, Gre\v sákova 6, 04001 Ko\v sice, SlovakiaAbstract: 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:
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