ROUGH QUASI-IDEALS IN REGULAR SEMI RINGS
Keywords:
quasi-k-ideals, approximations, equivalentAbstract
In this paper we study the notion of quasi-ideals and quasi-k-ideals in regular semirings and characterize quasi-ideals and quasi-k-ideals in terms of the rough approximations. Finally it is shown that a semiring is regular iff for any right k-ideal and left k-ideal of and it is established that is regular and are equivalent in semirings.
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. Coumaressane and V. S. Subha, Rough bi-ideals in near-rings, Proceedings of the International Workshop on Fuzzy Sets, Rough Sets, Uncertainty Analysis andApplications, NIT, Durgapur, India, November 21-25 (2011) 1-10.
B. Davvaz, Roughness in rings, Information Sciences, 164(2004) 147-163.
——, Rough sets in a fundamental ring, Bulletin of Iranian Mathematical Society,24(2)(1998) 49-61.
V. Gupta and J. N. Chaudhari, Prime ideals in semirings, Bulletin of the Malaysian
Mathematical Sciences Society,(2) 34(2) (2011) 417-421.
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.
N. Kuroki and J. N. Mordeson, Structure of rough sets and rough groups, Journal ofFuzzy Mathematics, 5(1)(1997) 183-191.
K. Osman and B. Davvaz, On the structure of rough prime (primary) ideals and roughfuzzy prime (primary) ideals in commutative rings, Information Sciences, 178 (2008),1343-1354.
Downloads
Published
How to Cite
Issue
Section
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.