A note on Dedekind and ZPI modules


TEKİR Ü.

ALGEBRA COLLOQUIUM, cilt.13, sa.1, ss.41-45, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Konu: 1
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1142/s1005386706000071
  • Dergi Adı: ALGEBRA COLLOQUIUM
  • Sayfa Sayıları: ss.41-45

Özet

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.