The Sum Operation and Llink Lattices

• Autorzy: Grygiel J. , Wojtylak P.
• Języki publikacji: EN

Abstrakty

EN

The sum operation, as introduced by Andrzej Wroński, is used to decompose any finite distributive lattice into its Boolean fragments. The decomposition is not unique but its maximal components are uniquely determined. We define an ordering relation between these maximal Boolean fragments of a given lattice and use this link ordering to describe the structure of the lattice.

Słowa kluczowe

EN

mesh networks; addition; distribution network

PL

sieci kratowe; sumowanie; sieć rozdzielcza

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 1999
• Tom: Vol. 6
• Strony: 23--28
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Grygiel J.

• Pedagogical University Institute of Mathematics Al.Armii Krajowej 13/15 Częstochowa 42-201

autor

Wojtylak P.

• Silesian University Institute of Mathematics Bankowa 14 Katowice 40-007

Bibliografia

• [1] Grätzer G., General Lattice Theory, Birkhaüser Verlag, 1978.
• [2] Grygiel J., The link lattices of finite distributive lattices, Reports on Mathematical Logic, to appear.
• [3] Grygiel J., Wojtylak P., The uniqueness of the decomposition of distributive lattices into sums of Boolean lattices, Reports on Mathematical Logic, to appear.
• [4] Jaśkowski S., Recherches sur le systéme de la logique intuitioniste, Actes du Congrés International de Philosophe Scientifique, VI Philosophie des Mathématiques, Actualites Scientifiqiés et Industrielles, 393 (1936), 58-61.
• [5] Kotas J., Wojtylak P., Finite distributive lattices as sums of Boolean algebras, Reports on Mathematical Logic, 29 (1995), 35-40.
• [6] Troelstra A.S., On intermediate propositional logic, Indagationes Mathematicae, 27 (1965), 141-152.
• [7] Wroński A., Remarks on intermediate logics wit h axioms containing only one variable, Reports on Mathematical Logic, 2(1974),63-76.