Modules Satisfying the Ascending Chain Condition on Radical Submodules

Abstract

An R-module M is called radical Noetherian if every ascending chain of radical submodules of M terminates. The class of radical Noetherian modules contains the class of Noetherian modules properly. Among other results, it is shown that an R-module M is radical Noetherian if and only if the set of minimal prime submodules of M is finite if and only if the set of radical submodule of M is finite.