Geodesic
Subalgebras and homomorphic images of algebras having the CEP and the WCIP
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 155-160

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MR Zbl
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.
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.
Classification : 08A30, 08B10
Keywords: CEP; WCIP; weak congruence; lattice 
Walendziak, Andrzej. Subalgebras and homomorphic images of algebras having the CEP and the WCIP. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 155-160. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a12/
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     zbl = {1049.08002},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a12/}
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