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- Title
Representing an isotone map between two bounded ordered sets by principal lattice congruences.
- Authors
Czédli, G.
- Abstract
For bounded lattices L1 and L2, let f:L1→L2<inline-graphic></inline-graphic> be a lattice homomorphism. Then the map Princ(f):Princ(L1)→Princ(L2)<inline-graphic></inline-graphic>, defined by con(x,y)↦con(f(x),f(y))<inline-graphic></inline-graphic>, is a 0-preserving isotone map from the bounded ordered set Princ(L1) of principal congruences of L1 to that of L2. We prove that every 0-preserving isotone map between two bounded ordered sets can be represented in this way. Our result generalizes a 2016 result of G. Grätzer from {0,1}<inline-graphic></inline-graphic>-preserving isotone maps to 0-preserving isotone maps.
- Subjects
LATTICE theory; ISOTONE shift; ABSTRACT algebra; HYPERFINE interactions; MATHEMATICS
- Publication
Acta Mathematica Hungarica, 2018, Vol 155, Issue 2, p332
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-018-0844-5