Authors: Czédli, Gábor
Šešelja, Branimir
Tepavčević, Andreja 
Title: On the semidistributivity of elements in weak congruence lattices of algebras and groups
Journal: Algebra Universalis
Volume: 58
Issue: 3
First page: 349
Last page: 355
Issue Date: 1-Jun-2008
Rank: M23
ISSN: 0002-5240
DOI: 10.1007/s00012-008-2076-y
Weak congruence lattices and semidistributive congruence lattices are both recent topics in universal algebra. This motivates the main result of the present paper, which asserts that a finite group G is a Dedekind group if and only if the diagonal relation is a join-semidistributive element in the lattice of weak congruences of G. A variant in terms of subgroups rather than weak congruences is also given. It is pointed out that no similar result is valid for rings. An open problem and some results on the join-semidistributivity of weak congruence lattices are also included.
Keywords: Dedekind group | Semidistributivity | Weak congruence lattice
Publisher: Springer Link
Project: NFSR of Hungary (OTKA), grant no. T 049433 and K 60148
Algebarske strukture i metode za procesiranje informacija, 144011
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, grant ”Lattice methods and applications”

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