Fuzzy weakly irreducible ideals of a ring

Document Type : Research Paper

Authors

1 Department of Mathematics, Dr.Vitthalrao Vikhe Patil College of Engineering,Ahmednagar 414001, India

2 Formerly of Department of Mathematics,Dr. Babasaheb Ambedkar Marathwada University, Aurangabad 431004, India

Abstract

In this paper, we introduce the concept of a fuzzy weakly irreducible ideal of a commutative ring R with identity.
This concept is a generalization of the concept of a fuzzy strongly irreducible ideal. Also, relationships between fuzzy maximal, fuzzy quasi primary and fuzzy weakly irreducible ideals in a ring are proved.

Keywords

References

[1] V. N. Dixit, R. Kumar and N. Ajmal, On fuzzy rings, Fuzzy Sets and Systems, 49 (1992), 205-213.
[2] R. Kumar, Fuzzy algebra, Publication Division, University of Delhi, Volume 1, 1993.
[3] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8(2) (1982), 133-139.
[4] D. S. Malik and J. N. Mordeson, Fuzzy maximal, radical and primary ideals of a ring, Information Sciences, 52 (1991), 253-250.
[5] T. K. Mukherjee and M. K. Sen, On fuzzy ideals of a ring (I), Fuzzy Sets and Systems, 21 (1987), 99-104.
[6] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[7] M. Samiei and H. Fazaeli Moghhimi, Weakly irreducible ideals, J. Algebra and Related Topics, 4(2) (2016), 9-17.
[8] T. Shah and M. Saeed, Fuzzy ideals in laskerian ring, Matematicki Vesnik 65, 1 (2013), 74-81.
[9] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
Journal of Hyperstructures
Volume 10, Issue 2
December 2021
Pages 118-128

Files

Share

How to cite

Statistics