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On the lattice of closed classes of modules
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova
Аннотация:
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.
Ключевые слова и фразы:
Closed class of modules, natural class, frame (Brouwerian lattice), pseudocomplement, boolean lattice.
MSC: 16D80,
16D90,
16D20 Поступила в редакцию: 21.07.2005
Язык публикации: английский
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