| Title of paper:
|
On the intuitionistic fuzzy polynomial ideals of a ring
|
| Author(s):
|
| P. K. Sharma
|
| Post Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
|
| pksharma@davjalandhar.com
|
| Gagandeep Kaur
|
| Research Scholar, IKG PT University, Jalandhar, Punjab, India
|
| taktogagan@gmail.com
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 1, pages 48–59
|
| Download:
|
 PDF (269 Kb Kb, File info)
|
| Abstract:
|
In this paper we introduce the notion of intuitionistic fuzzy polynomial ideal Ax of a polynomial ring R[x] induced by an intuitionistic fuzzy ideal A of a ring R, and obtain an isomorphism theorem of a ring of intuitionistic fuzzy cosets of Ax. It is shown that an intuitionistic fuzzy ideal A of a ring is an intuitionistic fuzzy prime if and only if Ax is an intuitionistic fuzzy prime ideal of R[x]. Moreover, we show that if Ax is an intuitionistic fuzzy maximal ideal of R[x], then A is an intuitionistic fuzzy maximal ideal of R but converse is not true.
|
| Keywords:
|
Intuitionistic fuzzy polynomial ideal, Intuitionistic fuzzy ideal, f-invariant, Intuitionistic fuzzy prime (maximal) ideal.
|
| AMS Classification:
|
03E72, 03F55, 13F20.
|
| References:
|
- Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
- Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Studies on Fuzziness and Soft Computing, 35, Springer Physica-Verlag, Heidelberg.
- Bakhadach, I., Melliani, S., Oukessou, M., & Chadli, S. L. (2016) Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring, Notes on Intuitionistic Fuzzy Sets, 22(2), 59– 63.
- Banerjee, B., & Basnet, D. K. (2003) Intuitionistic fuzzy subrings and ideals, The Journal of Fuzzy Mathematics, 11(1), 139–155.
- Biswas, R. (1989) Intuitionistic fuzzy subgroups, Math. Forum, 10, 37–46.
- Hur, K. , Kang, H. W., & Song, H. K. (2003) Intuitionistic Fuzzy Subgroups and Subrings, Honam Math J., 25(1), 19–41.
- Hur, K., Jang, S. Y., & Kang, H. W. (2005) Intuitionistic Fuzzy Ideals of a Ring, Journal of the Korea Society of Mathematical Education, Series B, 12(3), 193–209.
- Jun, Y. B., Ozturk, M. A., & Park, C. H. (2007) Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in ring, Information Science, 177, 4662–4677.
- Kim, C. B., Kim, H. K., & So, K. S. (2014) On the fuzzy polynomial ideals, Journal of Intelligent and Fuzzy Systems, 27, 487–494.
- Malik, D. S. (1991) Fuzzy Maximal, Radical, and Primary Ideals of a Ring, Information Sciences, 53, 237–250.
- Malik, D. S., & Mordeson, J. N. (1998) Fuzzy Commutative Algebra, World Scientific Publishing Co-Pvt. Ltd.
- Meena, K. (2017) Characteristic intuitionistic fuzzy subrings of an intuitionistic fuzzy ring, Advances in Fuzzy Mathematics, 12(2), 229–253.
- Meena, K., & Thomas, K. V. (2011) Intuitionistic L-Fuzzy Subrings, International Mathematical Forum, 12(52), 2561–2572.
- Sharma, P. K. (2011) Translates of intuitionistic fuzzy subring, International Review of Fuzzy Mathematics, 6(2), 77–84.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
