A representation theorem for certain boolean lattices

Abstract

Let R be an associative ring with 1 and R-tors the complete 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 .1; is a complete atomic boolean lattice then, there exists a left semiartinian ring R such that £ is lattice-isomorphic to R-tors.