Details
| Original language | English |
|---|---|
| Pages (from-to) | 399-418 |
| Number of pages | 20 |
| Journal | Algebra universalis |
| Volume | 62 |
| Issue number | 4 |
| Publication status | Published - 29 May 2010 |
Abstract
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
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Logic
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In: Algebra universalis, Vol. 62, No. 4, 29.05.2010, p. 399-418.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Characteristic triangles of closure operators with applications in general algebra
AU - Czédli, G.
AU - Erné, M.
AU - Šešelja, B.
AU - Tepavčević, A.
PY - 2010/5/29
Y1 - 2010/5/29
N2 - 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.
AB - 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.
KW - Algebraic lattice
KW - Characteristic triangle
KW - Continuous closure
KW - Dedekind group
KW - Diagram
KW - Normal subgroup
KW - Weak congruence lattice
UR - http://www.scopus.com/inward/record.url?scp=77954660608&partnerID=8YFLogxK
U2 - 10.1007/s00012-010-0059-2
DO - 10.1007/s00012-010-0059-2
M3 - Article
AN - SCOPUS:77954660608
VL - 62
SP - 399
EP - 418
JO - Algebra universalis
JF - Algebra universalis
SN - 0002-5240
IS - 4
ER -