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Title: Weak congruences of an algebra with the CEP and the WCIP (English)
Author: Walendziak, Andrzej
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 52
Issue: 1
Year: 2002
Pages: 117-127
Summary lang: English
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Category: math
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Summary: Here we consider the weak congruence lattice $C_{W}(A)$ of an algebra $A$ with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices. (English)
Keyword: weak congruence
Keyword: CEP
Keyword: WCIP
Keyword: semimodular lattice
Keyword: complemented lattice
MSC: 06C10
MSC: 06C15
MSC: 08A30
idZBL: Zbl 0998.08001
idMR: MR1885461
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Date available: 2009-09-24T10:49:38Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127706
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Reference: [7] B. Šešelja and A.  Tepavčevič: On CEP and semimodularity in the lattice of weak congruences.Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22 (1992), 95–106. MR 1295228
Reference: [8] G.  Vojvodič and B.  Šešelja: Subalgebras and congruences via diagonal relation.In: Algebra and Logic, Proc. of Sarajevo Conf, 1987, pp. 169–177. MR 1102051
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