@article {
author = {M. Abduldaim, Areej},
title = {Trivial Extension of π-Regular Rings},
journal = {Engineering and Technology Journal},
volume = {34},
number = {1B},
pages = {153-159},
year = {2016},
publisher = {University of Technology-Iraq},
issn = {1681-6900},
eissn = {2412-0758},
doi = {10.30684/etj.34.1B.17},
abstract = {In this paper we investigate if it is possible that the trivial extension ring T(R,R) inherit the properties of the ring R and present the relationship between the trivial extension T(R,M) of a ring R by an R-module M and theπ-regularity of Rby taking new concepts asπ-coherent rings and C-π-regular rings whichintroducedas extensions of the concept of π-regularrings. Moreover we studied the possibility of being the trivial extensionT(R,M) itselfπ-regular ring according to specific conditions. Thus we proved that if R is an Artinian ring, then the trivial extension T(R,R) is a π-regular ring. As well as ifthe trivial extension T(R,R) is a Noetherian π-regularring, then R is a π-regular ring. On the other hand we showed that if F is a field and M is an F-vector space with infinite dimension, then the trivial extension ring T(F,M) of F by M is C-π-regular ring.},
keywords = {Trivial extension ring,regular ring,Artinian ring,Noetherian ring},
url = {https://etj.uotechnology.edu.iq/article_112594.html},
eprint = {https://etj.uotechnology.edu.iq/article_112594_6d98539910be9b18fd260e4754445423.pdf}
}