Classification systems and their lattice
Sándor Radeleczki
Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002), p. 167-181 / Harvested from The Polish Digital Mathematics Library
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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent and Cls(L) is a partition lattice.

Publié le : 2002-01-01
EUDML-ID : urn:eudml:doc:287635 
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Sándor Radeleczki. Classification systems and their lattice. Discussiones Mathematicae - General Algebra and Applications, Tome 22 (2002) pp. 167-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1056/

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