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On Rings Whose Simple Singular R-Modules Are Flat, I | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 4, Volume 7, Issue 1, 2010, Pages 51-57 PDF (220.21 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2010.163846 | ||
| Authors | ||
| Raida D. Mahmood1; Abdullah M. Abdul-Jabbar2 | ||
| 1College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq | ||
| 2College of Science University of Salahaddin | ||
| Abstract | ||
| In this paper we investigate von Neumann regularity of rings whose simple singular right R-modules are flat. It is proved that a ring R is strongly regular if and only if R is a semiprime right quasi-duo ring whose simple singular right R-modules are flat. Moreover, it is shown that if R is a P. I.-ring whose simple singular right R-modules are flat, then R is a strongly p-regular ring. Finally, it is shown that if R is a right continuous ring whose simple singular right R-modules are flat, then R is a von Neumann regular ring. | ||
| Keywords | ||
| Semiprime; Flat; regular ring | ||
|
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