Keywords : regular rings


On Almost Weakly np – injective Rings

Raida D. Mahmood; Amaar M. Ghaze

AL-Rafidain Journal of Computer Sciences and Mathematics, 2018, Volume 12, Issue 2, Pages 25-30
DOI: 10.33899/csmj.2018.163575

The ring R is called right almost weakly np –injective, if for any , there exists a positive integer n and a left ideal  of R such that . In this paper, we give some characterization and properties of almost weakly np – injective rings. And we study the regularity of right almost weakly np – injective ring and in the same time, when every simple (simple singular) right R – module is almost weakly np – injective, we also give some properties of an R.
 

A Generalization of Von Neumann Regular Rings

Adil K. Jabbar

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 2, Pages 197-210
DOI: 10.33899/csmj.2009.163808

In this paper, we introduce a new ring which is a generalization of Von Neumann  regular rings and we call it a centrally regular ring. Several properties of this ring are proved and we have extended many properties of regular rings to centrally regular rings. Also we have determined some conditions under which regular and centrally regular rings are equivalent. 
 

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.
 

On Dual Rings

Nazar H. Shuker; Rani S. Younis

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 1, Pages 20-26
DOI: 10.33899/csmj.2004.164094

A ring R is called a right dual ring if rl(T) = T  for all right ideals T of R. The main  purpose of this  paper is to develop some basic properties of dual rings and to give the connection between dual rings, regular rings and strongly regular rings.