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Subalgebras and homomorphic images of algebras having the CEP and the WCIP

Andrzej Walendziak (2004)

Czechoslovak Mathematical Journal

In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.

The minimal closed monoids for the Galois connection End - Con

Danica Jakubíková-Studenovská, Reinhard Pöschel, Sándor Radelecki (2024)

Mathematica Bohemica

The minimal nontrivial endomorphism monoids M = End Con ( A , F ) of congruence lattices of algebras ( A , F ) defined on a finite set A are described. They correspond (via the Galois connection End - Con ) to the maximal nontrivial congruence lattices Con ( A , F ) investigated and characterized by the authors in previous papers. Analogous results are provided for endomorphism monoids of quasiorder lattices Quord ( A , F ) .

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