%0 Journal Article
%T Trivial Extension of π-Regular Rings
%J Engineering and Technology Journal
%I University of Technology-Iraq
%Z 1681-6900
%A M. Abduldaim, Areej
%D 2016
%\ 01/01/2016
%V 34
%N 1B
%P 153-159
%! Trivial Extension of π-Regular Rings
%K Trivial extension ring
%K regular ring
%K Artinian ring
%K Noetherian ring
%R 10.30684/etj.34.1B.17
%X 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.
%U https://etj.uotechnology.edu.iq/article_112594_6d98539910be9b18fd260e4754445423.pdf