PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 56(70), pp. 34--40 (1994)
Graphical compositions and weak congruences
Miroslav Plo\v s\v cicaMathematical 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
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