Keywords : reduced rings


The Graph of Annihilating Ideals

Nazar H. Shuker; Fryad H. Abdulqadir

AL-Rafidain Journal of Computer Sciences and Mathematics, 2018, Volume 12, Issue 1, Pages 41-46
DOI: 10.33899/csmj.2018.163569

Let R be a commutative ring with identity and AG(R) be the set of ideals with      non-zero annihilators. The annihilating ideal graph AG(R) is a graph of vertex set             AG (R)\{(0)}  and two distinct ideal vertices I  and J are adjacent if and only if  . In this paper , we establish a new fundamental properties of AG(R) as well as its connection with Γ(R).
 

On m-Regular Rings

Zubayda M. Ibraheem; Maha F. Khalaf

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 61-70
DOI: 10.33899/csmj.2012.163701

As a generalization of regular rings, we introduce the notion, of m-regular rings, that is for all , there is a fixed positive integer m such that  is a Von-Neumann regular element. Some characterization and basic properties of these rings will be given. Also, we study the relation-ship between them and Von-Neumann regular rings, -regular rings, reduced rings, locally rings, uniform rings and 2-primal rings.
 

On n-Weakly Regular Rings

Raida D. Mahammod; Mohammed Th. Al-Neimi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 53-59
DOI: 10.33899/csmj.2012.163700

As a generalization of right weakly regular rings, we introduce the notion of right n-weakly regular rings, i.e. for all aN(R), aaRaR. In this paper, first  give  various properties of right n-weakly regular rings. Also, we study the relation between such rings and reduced rings by adding some types of rings, such as NCI, MC2 and SNF rings.
 

On n - Regular Rings

Raida D. Mahmood; Mohammed Th. Youns

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 53-59
DOI: 10.33899/csmj.2011.163641

As a generalization of regular rings, that is a ring is called n-regular if  for all . In this paper, we first  give  various properties of n-regular rings. Also, we study the relation between such rings and reduced rings by adding some types of rings, such as NCI rings, and other types of rings.
 

Wnil-Injective Modules

Raida D. Mahmood; Husam Q. Mohammad

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 1, Pages 135-143
DOI: 10.33899/csmj.2010.163852

A right module M is called Wnil-injective if for any 0 ¹ a Î N( R ), there exists a positive integer n such that an ¹ 0 and any right R-homomorphism f : anR ® M can be extended to R ® M. In this paper , we first give and develope various properties of right Wnil-injective rings, by which, many of the known results are extended. Also, we study the relations between such rings and reduced rings by adding some types of rings, such as SRB-rings, and other types of rings.
 

On sπ-Weakly Regular Rings

Raida D. Mahmood; Abdullah M. Abdul-Jabbar

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 39-46
DOI: 10.33899/csmj.2008.163969

A ring R is said to be right(left) sp-weakly regular if for each a Î R and a positive integer n,  aΠ aR aR (aÎ R aR a). In this paper, we continue to study sp-weakly regular rings due to R. D. Mahmood and A. M. Abdul-Jabbar [8]. We first consider properties and basic extensions of sp-weakly regular rings, and we give the connection of sp-weakly regular, semi  p-regular and p-biregular rings.
 
 

On CS- Rings

Anas S. Youns AL-Mashhdanny; Mohammed Th. Youns AL-Neimi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 193-199
DOI: 10.33899/csmj.2008.163982

The main purpose of this paper is to study CS-rings. We give some properties of right CS-rings and the connection between such rings and reduced rings, regular rings, strongly regular rings, and S-weakly regular rings.
 

Rings in which Every Simple Right R-Module is Flat

Raida D. Mahmood

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 1, Pages 88-95
DOI: 10.33899/csmj.2004.164099

The objective of this paper is to initiate the study of rings in which each simple right R-module is flat, such rings will be called right SF-rings. Some important properties of right SF-rings are obtained. Among other results we prove that: If R is a semi prime ERT right SF-ring with zero socle, then R is a strongly regular ring.