Keywords : weakly regular rings

On WJCP-Injective Rings

Raida D. Mahmood; Shahla M. Khalil

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 4, Pages 13-19
DOI: 10.33899/csmj.2013.163542

As a generalization of right injective rings, we introduce the nation of right injective rings, that is for any right nonsingular element  of R, there exists a positive integer  and  and any right - homomorphism , there exists  such that  for all . In this paper, we first introduce and characterize a right injective rings . Next , connection between such ring and quasi regular rings and weakly regular 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 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 Weakly Regular Rings and SSF-rings

Raida D. Mahmood

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 55-59
DOI: 10.33899/csmj.2006.164035

In this work we consider weakly regular rings whose simple singular right R-Modules are flat. We also consider the condition (*): R satisfies L(a)Ír(a) for any aÎR. We prove that if R satisfies(*) and whose simple singular right R-module are flat, then Z (R)  the center of  R  is a von    Neunann regular ring. We also show that a ring R either satisfies (*) or a strongly right bounded ring in which every simple singular right R-module is flat, then  R is reduced weakly regular rings.