RADICALS OF SUBMODULES IN MODULES

Abstract

The radical rad N of a submodule N of a module M is defined as the intersection of all prime submodules containing N. In this paper, we show that if the ideals (N : M) and (L : M) are comaximal then the equality rad (N boolean AND L) = rad N boolean AND rad L holds. We also discuss some properties of finitely generated R-modules.