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IMI/Publicaţii/BASM/Ediţii/BASM n.2 (48), 2005/

On the lattice of closed classes of modules.

Authors: Caşu Alexei

Abstract

The family of closed classes of left R-modules R-cl (i.e. of classes which can be described by sets of left ideals of R) is transformed in a lattice and its properties are studied. The lattice R-cl is a frame (or Brouwerian lattice, or Heyting algebra). For every class K ∈ R -cl its pseudocomplement K* in R-cl is characterized. The skeleton of R-cl (i.e. the set of classes of the form K*, R ∈ R -cl) coincides with the boolean lattice R-nat of natural classes of R-Mod. In parallels the isomorphic with R-cl lattice R-Cl of closed sets of left ideals of R is investigated, exposing some similar properties.

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