Multiplication modules with prime spectrum

Abstract

The subject of this paper is the Zariski topology on a multiplication module M over a commutative ring R.We find a characterization for the radical submodule radM(0) and also show that there are proper ideals I1; :::; In of Rsuch that radM(0) = radM((I1:::In)M) . Finally, we prove that the spectrum Spec(M) is irreducible if and only if Mis the finite sum of its submodules, whose T -radicals are prime in M.