ROUGH k-IDEALS IN SEMIRINGS

Authors

  • Dr. V.S Subha Assistant Professor, Department of Mathematics Annamalai University, Annamalai Nagar

Keywords:

Semirings;, congruence relation, k-ideals

Abstract

In this paper we introduce the notions of k-ideals and k-closure in semirings. We have shown that is a k-ideal of a semiring if and only if it is a rough k-ideal of . We have also shown that if and are left(right) ideals of a bemiring then is a rough ideal of . he theory of rough set was first introduced by Pawlak[9,10]. Rough set theory deals with inexact, uncertain or vague knowledge. It has recently been fascinated by researchers who work in both real life applications and theoretical developments. Rough set theory is an extension of set theory. It has many practical applications in areas such as data classification, data analysis, machine learning and knowledge discovery.

References

R. Biswas and S. Nanda, Rough groups and rough subgroups, Bulletin of the Polish Academy of Sciences, Mathematics, 42(3)(1994) 251-254.

S. Bourne, The jacobson radical of a semiring, Proc. Natl. Acad. Sci. USA, 37 (1951) 163-170.

B. Davvaz, Roughness in rings, Information Sciences, 164(2004) 147-163.

K. Is´eki, Ideals in semirings, Proceedings of the Japan Academy, 34(1)(1958) 29-31.

N. Kuroki, Rough ideals in semigroups, Information Sciences ,100(1997) 139-163.

N. Kuroki and P. P. Wang, The lower and upper approximations in a fuzzy group, Information Sciences, 90 (1996) 203-220.

Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences, 11(5)(1982) 341-356.

Z. Pawlak and A.Skowron, Rough sets: some extensions, Information Sciences, 177 (2007) 28-40.

N. Thillaigovindan, S. Coumaressane and V. S. Subha, Rough prime ideals in near-rings, Proceedings of the International Workshop on Fuzzy Sets, Rough Sets, Uncertainty Analysis and Applications, NIT, Durgapur, India, November 21-25 (2011) 11-18.

Downloads

Published

30-06-2014

How to Cite

Subha, D. V. (2014). ROUGH k-IDEALS IN SEMIRINGS. International Journal for Research Publication and Seminar, 5(1), 117–126. Retrieved from https://jrps.shodhsagar.com/index.php/j/article/view/48

Issue

Vol. 5 No. 1 (2014): Volume 5 | Issue 1 | Jan-Jun 2014

Section

Original Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Re-users must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. This license allows for redistribution, commercial and non-commercial, as long as the original work is properly credited.