Generalization of short modules
Author
Source
The Arabian Journal for Science and Engineering. Section A, Science
Issue
Vol. 32, Issue 1A (31 Jan. 2007), pp.121-127, 7 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
2007-01-31
Country of Publication
Saudi Arabia
No. of Pages
7
Main Subjects
Topics
Abstract AR
سوف نبرهن في هذا البحث أنه إذا كانت R حلقة نوثيرية محلية تبادلية فإن M قياس – R يكون (تقريبا) قصيرا و ملازما فقط إذا كان من نوع نوثيري.
و كذلك مدى (Dedekind) R و M قياس – R تكون M (تقريبا) قصيرا فقط إذا كانت M نوثيري أو كانت M تحتوي قياسا جزيئا N يكون نوثيري بحيث يكون M/N (تقريبا) قصيرا و غلافا ضمنيا لمقياس – R البسيط.
Abstract EN
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.
American Psychological Association (APA)
Bilhan, G.. 2007. Generalization of short modules. The Arabian Journal for Science and Engineering. Section A, Science،Vol. 32, no. 1A, pp.121-127.
https://search.emarefa.net/detail/BIM-358741
Modern Language Association (MLA)
Bilhan, G.. Generalization of short modules. The Arabian Journal for Science and Engineering. Section A, Science Vol. 32, no. 1A (Jan. 2007), pp.121-127.
https://search.emarefa.net/detail/BIM-358741
American Medical Association (AMA)
Bilhan, G.. Generalization of short modules. The Arabian Journal for Science and Engineering. Section A, Science. 2007. Vol. 32, no. 1A, pp.121-127.
https://search.emarefa.net/detail/BIM-358741
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 127
Record ID
BIM-358741
