This article is cited in 2 papers

On the lattice of closed classes of modules

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

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 ${\EuScript K}\in R$-cl its pseudocomplement ${\EuScript K}^*$ in $R$-cl is characterized. The skeleton of $R$-cl (i.e. the set of classes of the form ${\EuScript K}^*$, ${\EuScript K}\in R$-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.

Keywords and phrases: Closed class of modules, natural class, frame (Brouwerian lattice), pseudocomplement, boolean lattice.

MSC: 16D80, 16D90, 16D20

Received: 21.07.2005

Language: English

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