Authors: Czédli, Gábor
Erné, Marcel
Šešelja, Branimir
Tepavčević, Andreja 
Title: Characteristic triangles of closure operators with applications in general algebra
Journal: Algebra Universalis
Volume: 62
Issue: 4
First page: 399
Last page: 418
Issue Date: 1-Sep-2009
Rank: M23
ISSN: 0002-5240
DOI: 10.1007/s00012-010-0059-2
Our aim is to investigate groups and their weak congruence lattices in the abstract setting of lattices L with (local) closure operators C in the categorical sense, where L is regarded as a small category and C is a family of closure maps on the principal ideals of L. A useful tool for structural investigations of such lattices with closure is the so-called characteristic triangle, a certain substructure of the square L2. For example, a purely order-theoretical investigation of the characteristic triangle shows that the Dedekind groups (alias Hamiltonian groups) are precisely those with modular weak congruence lattices; similar results are obtained for other classes of algebras.
Keywords: Algebraic lattice | Characteristic triangle | Continuous closure | Dedekind group | Diagram | Normal subgroup | Weak congruence lattice
Publisher: Springer Link
Project: NFSR of Hungary (OTKA), Grant No. T 049433 and K 60148
Provincial Secretariat for Science and Technological Development, Grant “Lattice methods and applications”
Algebarske strukture i metode za procesiranje informacija, 144011

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