A representation theorem for certain Boolean lattices.

Ríos Montes, José. "A representation theorem for certain Boolean lattices.." Publicacions Matemàtiques 32.1 (1988): 111-113. <http://eudml.org/doc/41026>.

@article{RíosMontes1988,
abstract = {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.},
author = {Ríos Montes, José},
journal = {Publicacions Matemàtiques},
keywords = {Retículos; Torsión; Brouwerian lattice; hereditary torsion theories on the category of left R-modules; complete atomic Boolean lattice; left semiartinian ring},
language = {eng},
number = {1},
pages = {111-113},
title = {A representation theorem for certain Boolean lattices.},
url = {http://eudml.org/doc/41026},
volume = {32},
year = {1988},
}

TY - JOUR
AU - Ríos Montes, José
TI - A representation theorem for certain Boolean lattices.
JO - Publicacions Matemàtiques
PY - 1988
VL - 32
IS - 1
SP - 111
EP - 113
AB - 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.
LA - eng
KW - Retículos; Torsión; Brouwerian lattice; hereditary torsion theories on the category of left R-modules; complete atomic Boolean lattice; left semiartinian ring
UR - http://eudml.org/doc/41026
ER -