Lattices respecting convex decompositions, II

• Autorzy: Beran L. , Saarimäki M.
• Języki publikacji: EN

Abstrakty

EN

Let (L1,L2) be a convex decomposition of a lattice L. We prove that L is a lattice satisfying the atomic covering property provided L1 and L2 possess the same property. Moreover we show that L satisfies the general disjointness property (GD) whenever L1 satisfies GD and L2 is a modular lattice or whenever L1 is a modular lattice with 0 and L2 satisfies GD.

Słowa kluczowe

EN

convex decomposition; atomic convering condition; modular lattice

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 455--460
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Beran L.

• Department of Algebra, Charles University, Sokolovská 83, 186 00 Prague 8, Czech Republic

autor

Saarimäki M.

• Department of Mathematics, University of Jyväskylä, P. O. Box 35, Fin - 40351 Jyväskylä, Finland

Bibliografia

• [1] L. Beran, Distributivity via Boolean Algebras, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), 191-206.
• [2] L. Beran, M. Saarimäki, Lattices respecting convex decompositions, I, Demonstratio Math. 35 (2002), 217-224.
• [3] F. Maeda, S. Maeda, Theory of Symmetric Lattices, Springer, Berlin, 1970.
• [4] M. Saarimäki, P. Sorjonen, On Banaschewski functions in lattices, Algebra Universalis 28 (1991), 103-118.
• [5] M. Saarimäki, Disjointness of lattice elements, Math. Nachr. 159 (1992), 169-174.
• [6] M. Saarimäki, Disjointness and complementedness in upper continuous lattices, University of Jyväskylä, Report 78 (1998).