On schemes for congruence distributivity
type: Item
instance of: scholarly article
title: On schemes for congruence distributivity
zbMATH Open document ID: 1062.08002
DOI: 10.2478/BF02475233
author: Ivan Chajda
author: Radomír Halaš
published in: Central European Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: \textit{H. P. Gumm} [Mem. Am. Math. Soc. 286 (1983; Zbl 0547.08006)] introduced the diagrammatic scheme known as the Shifting Lemma to characterize congruence modularity. This paper considers congruence distributivity for a single algebra and introduces schemes that characterize congruence distributivity within an \(n\)-permutable algebra, with particular emphasis on the case of 3-permutability. The paper ends with a Mal'tsev condition which characterizes the Triangular Scheme (used by the first author to characterize congruence distributivity in congruence permutable algebras [\textit{I. Chajda}, East-West J. Math. 3, 79--80 (2001; Zbl 1007.08002); \textit{I. Chajda} and \textit{E. K. Horváth}, Acta Sci. Math. 68, 29--35 (2002; Zbl 0997.08001)]).
reviewed by: Sheila Oates-Williams
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 2143686
zbMATH Keywords: congruence distributivity
zbMATH Keywords: congruence 3-permutability
zbMATH Keywords: congruence \(n\)-permutability
zbMATH Keywords: diagrammatic scheme
zbMATH Keywords: triangular scheme
MaRDI profile type: Publication
cites work: Q4547877
cites work: Q4780300
cites work: A scheme for congruence semidistributivity
cites work: Q4650936
cites work: The shifting lemma and shifting lattice identities
cites work: Geometrical methods in congruence modular algebras
cites work: Algebras Whose Congruence Lattices are Distributive.
full work available at URL: https://doi.org/10.2478/bf02475233
OpenAlex ID: W2036727965
description: scientific article; zbMATH DE number 2143686