Generalization of short modules

Bilhan G.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, cilt.32, sa.1A, ss.121-127, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 1A
  • Basım Tarihi: 2007
  • Dergi Adı: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.121-127
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

It is proved that, if R is a commutative local Noetherian ring, then an R-module M is (almost) short and coatomic if and only if it is Noetherian. Also, for a Dedekind Domain R and R-module M, M is (almost) short if and only if M is Noetherian or M contains a Noetherian submodule N such that M/N is (almost) short and is the injective hull of a simple R-module.