Envelopes and Weakly Radicals of Submodules
Abstract
Let
N
be a submodule of a finitely generated module
M
over a Noetherian ring. A method for the computation of the submodule generated by the envelope of
N
is given. The relations between weakly prime submodules and their envelopes are investigated. Using these relations, a description of the weakly radical of a submodule is obtained. The results are illustrated by examples.