A note on semi-principal ideal rings
Source
The Arabian Journal for Science and Engineering. Section A, Science
Issue
Vol. 22, Issue 2A (31 Jul. 1997), pp.195-206, 12 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
1997-07-31
Country of Publication
Saudi Arabia
No. of Pages
12
Main Subjects
Abstract EN
A ring R is said to be a Principal Ideal Ring (PIR) iff every ideal of R is principal, and is said to be a semi-Principal Ideal Ring (semi-PIR) iff every ideal of R is a direct sum of principal ideals.
Using elementary techniques, we obtain characterizations of PIR’s and semi-PIR’s of the type R = 1[T]/I where / = (f(T)) is the ideal generated by f(T) and where f(T) is a product of two distinct monic irreducible polynomials.
As a corollary, we obtain a result of Reiner characterizing semi-PIR’s of the type TL [71/(7^—1), with p prime.
American Psychological Association (APA)
Habib, Jibril& Hujjah, Muwaffaq. 1997. A note on semi-principal ideal rings. The Arabian Journal for Science and Engineering. Section A, Science،Vol. 22, no. 2A, pp.195-206.
https://search.emarefa.net/detail/BIM-390017
Modern Language Association (MLA)
Habib, Jibril& Hujjah, Muwaffaq. A note on semi-principal ideal rings. The Arabian Journal for Science and Engineering. Section A, Science Vol. 22, no. 2A (Jul. 1997), pp.195-206.
https://search.emarefa.net/detail/BIM-390017
American Medical Association (AMA)
Habib, Jibril& Hujjah, Muwaffaq. A note on semi-principal ideal rings. The Arabian Journal for Science and Engineering. Section A, Science. 1997. Vol. 22, no. 2A, pp.195-206.
https://search.emarefa.net/detail/BIM-390017
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 206
Record ID
BIM-390017
