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On MP-Rings | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 14, Volume 14, Issue 1, 2020, Pages 35-40 PDF (888.56 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2020.164797 | ||
| Authors | ||
| Raida D. Mahmood1; Azhar M. Hajo2 | ||
| 1College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq | ||
| 2Department of Mathematics College of Computer Science and Mathematics University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| An ideal I of a ring R is said to be right (left) Pure if for every , there is such that . A ring R is said to be right (left) MP-ring, if every maximal right (left) ideal of R is a left (right) pure. In this paper have been studied some new properties of MP-rings, there connections with strongly regular rings. Some of the main result of the present work are as follows: 1- Let R be aright MP-ring, r(a) is a W-ideal for all then a- Every essential ideal is a direct summand. b- R is strongly regular ring. 2- Let R be aright MP-ring. If R is right almost abelian left NBF ring, then R is strongly regular. | ||
| Keywords | ||
| MP-ring; strongly regular; W-ideal; NBF-ring | ||
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