Trivial extension of π-regular rings
Other Title(s)
التمديد التافه للحلقات المنظمة من النمط π
Author
Source
Engineering and Technology Journal
Issue
Vol. 34, Issue 1B (31 Jan. 2016), pp.153-159, 7 p.
Publisher
Publication Date
2016-01-31
Country of Publication
Iraq
No. of Pages
7
Main Subjects
Abstract EN
In this paper we investigate if it is possible that the trivial extension ring ???, ?? inherit the properties of the ring ? and present the relationship between the trivial extension ???, ?? of a ring ? by an ?-module ? and the ?-regularity of ? by taking new concepts as ?-coherent rings and ?- ?-regular rings which introduced as extensions of the concept of ?-regularrings.
Moreover we studied the possibility of being the trivial extension ???, ?? itself ?-regular ring according to specific conditions.
Thus we proved that if ? is an Artinian ring, then the trivial extension ???, ?? is a ?-regular ring.
As well as if the trivial extension ???, ?? is a Noetherian ?-regular ring, then ? is a ?-regular ring.
On the other hand we showed that if ? is a field and ? is an ?-vector space with infinite dimension, then the trivial extension ring ???, ?? of ? by ? is ?-?-regular ring.
American Psychological Association (APA)
Abd al-Dayim, Arij Musab. 2016. Trivial extension of π-regular rings. Engineering and Technology Journal،Vol. 34, no. 1B, pp.153-159.
https://search.emarefa.net/detail/BIM-674088
Modern Language Association (MLA)
Abd al-Dayim, Arij Musab. Trivial extension of π-regular rings. Engineering and Technology Journal Vol. 34, no. 1B (2016), pp.153-159.
https://search.emarefa.net/detail/BIM-674088
American Medical Association (AMA)
Abd al-Dayim, Arij Musab. Trivial extension of π-regular rings. Engineering and Technology Journal. 2016. Vol. 34, no. 1B, pp.153-159.
https://search.emarefa.net/detail/BIM-674088
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 158-159
Record ID
BIM-674088