A note on Dedekind and ZPI modules
ALGEBRA COLLOQUIUM, cilt.13, sa.1, ss.41-45, 2006 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 13 Sayı: 1
- Basım Tarihi: 2006
- Doi Numarası: 10.1142/s1005386706000071
- Dergi Adı: ALGEBRA COLLOQUIUM
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.41-45
- Marmara Üniversitesi Adresli: Evet
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.