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Some Preserved Properties under Localization, S-Prime Radicals and S-Minimal Prime Ideals
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 166 - Number 7 |
| Year of Publication: 2017 |
| Authors: Adil Kadir Jabbar, Asmaa Ghazi Jameel |
10.5120/ijca2017914057
|
Adil Kadir Jabbar, Asmaa Ghazi Jameel . Some Preserved Properties under Localization, S-Prime Radicals and S-Minimal Prime Ideals. International Journal of Computer Applications. 166, 7 ( May 2017), 4-9. DOI=10.5120/ijca2017914057
Abstract
In this paper we prove some properties of ideals that are preserved under localization. Also, we establish several one to one correspondences between certain types of ideals in the ring and its localization at multiplicative systems. We introduce two concepts such as S-prime radical and S-minimal prime ideals and the relations of S-prime radical with the prime radical and Jacobson radical of a ring under localization are determined. Also, we prove a one to one correspondence between S-minimal primal ideals of a given ideal A of a ring R and the minimal prime ideals of the ideal A_P of R_P, where P is a prime ideal of R.
References
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