A note on Dedekind and ZPI modules

Abstract

Let R be a domain. A non-zero R-module M is called a Dedekind module if every submodule N of M such that N not equal M either is prime or has a prime factorization N = P-1,(P2PnN)-P-...*, where P-1, P-2,..., P-n are prime ideals of R and N* is a prime submodule in M. When R is a ring, a non-zero R-module M is called a ZPI module if every submodule N of M such that N not equal M either is prime or has a prime factorization. The purpose of this paper is to introduce interesting and useful properties of Dedekind and ZPI modules.