A representation theorem for certain Boolean lattices

Autores: José Ríos Montes
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 32, Nº 1, 1988, págs. 111-113
Idioma: inglés
DOI: 10.5565/publmat_32188_09
Títulos paralelos:
- Un teorema de representación para ciertos retículos booleanos
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Resumen
- 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.