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On MLGP- Rings | ||
| AL-Rafidain Journal of Computer Sciences and Mathematics | ||
| Article 11, Volume 13, Issue 2, 2019, Pages 61-66 PDF (313.56 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.33899/csmj.2020.163521 | ||
| Authors | ||
| Raida D. mahmood; Ebtehal S. Mageed | ||
| College of Computer Sciences and Mathematics University of Mosul, Mosul, Iraq | ||
| Abstract | ||
| An ideal K of a ring R is called right (left) generalized pure (GP -ideal) if for every a ∈ K, there exists m ∈ Z+, and b ∈ K such that am = am b ( am = b am) . A ring R is called MLGP-ring if every right maximal ideal is left GP-ideal. In this paper have been studied some new properties of MLGP-rings and the relation between this rings and strongly π-regular rings some of the main result of the present work are as follows: 1- Let R be a local ,MLGP and SXM ring. Then: (a) J (R) = 0. (b) If R is NJ-ring. Then r(am) is a direct sum and for all ∈ R, m ∈ Z+. 2- Let R be a local, SXM and NJ-ring . Then R is strongly π-regular if and only if R i LGP. | ||
| Keywords | ||
| NJ Rings; SXM rings; local strongly regular rings; pure ideals | ||
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