Keywords : pure ideals


On MLGP- Rings

Raida D. mahmood; Ebtehal S. Mageed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2019, Volume 13, Issue 2, Pages 61-66
DOI: 10.33899/csmj.2020.163521

An ideal K of a ring R is called right (left) generalized pure (GP -ideal) if for every a ∈ K, there exists m ∈ Z+, and b ∈ K such that  am = am b ( am = b am) . A ring R is called MLGP-ring if every right maximal ideal is left GP-ideal. In this paper have been studied some new properties of MLGP-rings and the relation between this rings and strongly π-regular rings some of the main result of the present work are as follows:
1- Let R be a local ,MLGP and  SXM ring. Then:
(a)  J (R) = 0.
(b)  If R is NJ-ring. Then r(am) is a direct sum and for all ∈ R,  m ∈ Z+.
2- Let R be a local, SXM and NJ-ring . Then R is strongly π-regular if and only if R i LGP. 

On GP- Ideals

Raida D. Mahmood; Shahla M. Khalil

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 3, Pages 57-63
DOI: 10.33899/csmj.2009.163821

In this work we give some new properties of GP- ideals as well as the relation between GP- ideals, - π regular and simple ring. Also we consider rings with every principal ideal are GP- ideals and establish relation between such rings with strongly  regular and local rings.
 

Maximal Generalization of Pure Ideals

Raida D. Mahmood; Awreng B. Mahmood

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 21-27
DOI: 10.33899/csmj.2008.163946

The purpose of this paper is to study the class of the rings for which every maximal right ideal is left GP-ideal. Such rings are called MGP-rings and give some of their basic properties as well as the relation between
MGP-rings, strongly regular ring, weakly regular ring and kasch ring.
 

On Rings whose Maximal Essential Ideals are Pure

Raida D. Mahmood; Awreng B. Mahmood

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 1, Pages 57-62
DOI: 10.33899/csmj.2007.163995

This paper introduces the notion of a right MEP-ring (a ring in which every maximal essential right ideal is left pure) with some of their basic properties; we also give necessary and sufficient conditions for MEP – rings to be strongly regular rings and weakly regular rings.