Geodesic
On the lattice of closed classes of modules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 43-50

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{BASM_2005_2_a1,
     author = {A. I. Kashu},
     title = {On the lattice of closed classes of modules},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {43--50},
     publisher = {mathdoc},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2005_2_a1/}
}
TY  - JOUR
AU  - A. I. Kashu
TI  - On the lattice of closed classes of modules
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2005
SP  - 43
EP  - 50
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2005_2_a1/
LA  - en
ID  - BASM_2005_2_a1
ER  - 
%0 Journal Article
%A A. I. Kashu
%T On the lattice of closed classes of modules
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2005
%P 43-50
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2005_2_a1/
%G en
%F BASM_2005_2_a1
A. I. Kashu. On the lattice of closed classes of modules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2005), pp. 43-50. http://geodesic.mathdoc.fr/item/BASM_2005_2_a1/