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| Titel: |
Some simple extensions of Eulerian lattices |
| Auteur: |
A. Vethamanickam R. Subbarayan |
| Verschenen in: |
Acta mathematica Universitatis Comenianae |
| Paginering: | Jaargang LXXIX (2010) nr. 1 pagina's 47-54 |
| Jaar: |
2010 |
| Inhoud: |
Let L be a lattice. If K is a sublattice of L, then L is called an extension of K. Lattice extension concept was elaborately studied by G. Grätzer and E. T. Schmidt in their papers [6], [7], [9], [10]. A lattice L is said to be simple if it has no non-trivial congruences. A finite graded poset P is said to be Eulerian if its Möbius function assumes the value μ(x, y) = (-1)l(x, y) for all x <FONT SIZE='3' FACE='Symbol'>£</FONT> y in P, where l(x, y) = ρ(y) - ρ(x) and ρ is the rank function on P. In this paper, we exhibit various possible Eulerian extensions which are simple for any given Eulerian lattice L and we prove that there exists a congruence-preserving extension of an Eulerian lattice. The cubic extension of a lattice was defined by G. Grätzer and E. T. Schmidt in [11].We show that the cubic extension becomes a congruence-preserving extension when the lattice is Eulerian. |
| Uitgever: |
Acta Mathematica Universitatis Comenianae (provided by DOAJ) |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 57 van 68 gevonden artikelen
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