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Title: A note on triangular schemes for weak congruences (English)
Author: Chajda, Ivan
Author: Šešelja, Branimir
Author: Tepavčević, Andreja
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 3
Year: 2005
Pages: 683-690
Summary lang: English
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Category: math
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Summary: Some geometrical methods, the so called Triangular Schemes and Principles, are introduced and investigated for weak congruences of algebras. They are analogues of the corresponding notions for congruences. Particular versions of Triangular Schemes are equivalent to weak congruence modularity and to weak congruence distributivity. For algebras in congruence permutable varieties, stronger properties—Triangular Principles—are equivalent to weak congruence modularity and distributivity. (English)
Keyword: triangular scheme
Keyword: triangular principle
Keyword: weak congruence
Keyword: weak congruence modularity
Keyword: weak congruence distributivity
MSC: 08A05
MSC: 08A30
idZBL: Zbl 1081.08004
idMR: MR2153092
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Date available: 2009-09-24T11:26:37Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/128012
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Reference: [1] I.  Chajda: A note on the Triangular Scheme.East-West J.  Math. 3 (2001), 79–80. Zbl 1007.08002, MR 1866645
Reference: [2] I.  Chajda and E. K. Horváth: A triangular scheme for congruence distributivity.Acta Sci. Math. (Szeged) (to appear). MR 1916565
Reference: [3] I.  Chajda, G.  Czédli and E. K. Horváth: Shifting lemma and shifting lattice identities.Preprint. MR 2026826
Reference: [4] H. P.  Gumm: Geometrical methods in congruence modular algebras.Mem. Am. Math. Soc. No. 286, 1983. Zbl 0547.08006, MR 0714648
Reference: [5] B. Jónsson: Algebras whose congruence lattices are distributive.Math. Scand. 21 (1967), 110–121. MR 0237402
Reference: [6] B. Šešelja and A.  Tepavčević: Weak Congruences in Universal Algebra.Institute of Mathematics, Novi Sad, 2001. MR 1878678
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