Generalization of short modules

Bilhan G.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.32, no.1A, pp.121-127, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1A
  • Publication Date: 2007
  • Journal Name: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.121-127
  • Dokuz Eylül University Affiliated: Yes

Abstract

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.