A note on Dedekind and ZPI modules

TEKİR Ü.

ALGEBRA COLLOQUIUM, vol.13, no.1, pp.41-45, 2006 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1142/s1005386706000071
  • Journal Name: ALGEBRA COLLOQUIUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.41-45
  • Marmara University Affiliated: Yes

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.