Let R be an associative ring with 1 and R-tors the somplete Brouwerian lattice of all hereditary torsion theories on the category of left R-modules. A well known result asserts that R is a left semiartinian ring iff R-tors is a complete atomic Boolean lattice. In this note we prove that if L is a complete atomic Boolean lattice then there exists a left semiartinian ring R such that L is lattice-isomorphic to R-tors.
@article{urn:eudml:doc:41026,
title = {A representation theorem for certain Boolean lattices.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {111-113},
zbl = {0651.06003},
mrnumber = {MR0939774},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41026}
}
Ríos Montes, José. A representation theorem for certain Boolean lattices.. Publicacions Matemàtiques, Tome 32 (1988) pp. 111-113. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41026/