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Reseach Article

Some Preserved Properties under Localization, S-Prime Radicals and S-Minimal Prime Ideals

by Adil Kadir Jabbar, Asmaa Ghazi Jameel
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

@article{ 10.5120/ijca2017914057,
author = { Adil Kadir Jabbar, Asmaa Ghazi Jameel },
title = { Some Preserved Properties under Localization, S-Prime Radicals and S-Minimal Prime Ideals },
journal = { International Journal of Computer Applications },
issue_date = { May 2017 },
volume = { 166 },
number = { 7 },
month = { May },
year = { 2017 },
issn = { 0975-8887 },
pages = { 4-9 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume166/number7/27679-2017914057/ },
doi = { 10.5120/ijca2017914057 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T00:13:02.498741+05:30
%A Adil Kadir Jabbar
%A Asmaa Ghazi Jameel
%T Some Preserved Properties under Localization, S-Prime Radicals and S-Minimal Prime Ideals
%J International Journal of Computer Applications
%@ 0975-8887
%V 166
%N 7
%P 4-9
%D 2017
%I Foundation of Computer Science (FCS), NY, USA
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
  1. Burton, D. M. 1970. A First Course in Rings and Ideals. Addison-Wesley Publishing Company.
  2. Darani, A. Y. 2011. Almost Primal Ideals in Commutative Rings. Chiang Mai J. Sci., 38(2), 161-165.
  3. Jabbar, A. K., Hamaali, P. M. and Hasan, K. A. 2012. Some Properties of Almost Primal and n-Almost Primal Ideals in Commutative Rings. Pioneer Journal of Algebra, Number Theory and its Applications, Volume 4, Number 1, 41-60.
  4. Larsen, M. D. and McCarthy, P. J. 1971. Multiplicative Theory of Ideals. Academic Press, New York and London.
  5. Wisbauer, R. 1991. Foundations of Module and Ring Theory. Gordon and Breach Science Publishers, Reading.
Index Terms

Computer Science
Information Sciences

Keywords

Multiplicative system Localization of a ring S-prime radical S-minimal prime ideal S-semisimple ring and S-Jacobson radical (Srad(R)).