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 | Abstract: | 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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