Modules Whose Maximal Submodules Have Τ-Supplements

Abstract

Let R be a ring and tau be a preradical for the category of left R-modules. In this paper, we study on modules whose maximal submodules have tau-supplements. We give some characterizations of these modules interms their certain submodules, so called tau-localsubmodules. For some certain preradicals tau, i.e. tau=delta and idempotent tau, we prove that every maximal submodule of M has a tau-supplement if and only if every cofinite submodule of M has a tau-supplement. For a radical tau onR-Mod, we prove that, forevery R-module every submodule is a tau-supplement if and only if R/tau(R) is semisimple and tau is hereditary