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Issue:On the intuitionistic fuzzy polynomial ideals of a ring

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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
DOI: https://doi.org/10.7546/nifs.2018.24.1.48-59
Download:  PDF (269 Kb  Kb, 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.
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