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Issue:On the translational invariant intuitionistic fuzzy subset of a Γ-ring: Difference between revisions

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  | format          = PDF
  | format          = PDF
  | size            = 212 Kb
  | size            = 212 Kb
  | abstract        = In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their
  | abstract        = In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an ''A<sub>γ</sub>''-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.
properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an ''A<sub>γ</sub>''-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.
  | keywords        = Γ-Ring, Translational invariant intuitionistic fuzzy subset (TIIFS), f-invariant intuitionistic fuzzy subset, ''A<sub>γ</sub>''-unit, ''A<sub>γ</sub>''-prime element.
  | keywords        = Γ-Ring, Translational invariant intuitionistic fuzzy subset (TIIFS), f-invariant intuitionistic fuzzy subset, ''A<sub>γ</sub>''-unit, ''A<sub>γ</sub>''-prime element.
  | ams            = 16Y99, 03F55, 03G25
  | ams            = 16Y99, 03F55, 03G25

Latest revision as of 07:36, 6 April 2022

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http://ifigenia.org/wiki/issue:nifs/28/1/11-22
Title of paper: On the translational invariant intuitionistic fuzzy subset of a Γ-ring
Author(s):
Hem Lata
Research Scholar, Lovely Professional University, Phagwara, Punjab, India
goyalhema1986@gmail.com
P. K. Sharma
Post Graduate, Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 1, pages 11–22
DOI: https://doi.org/10.7546/nifs.2022.28.1.11-22
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Abstract: In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we prove that every homomorphic image of a prime ideal of a Γ-ring generated by an Aγ-prime element and translational invariant and f-invariant intuitionistic fuzzy subset is also a prime ideal.
Keywords: Γ-Ring, Translational invariant intuitionistic fuzzy subset (TIIFS), f-invariant intuitionistic fuzzy subset, Aγ-unit, Aγ-prime element.
AMS Classification: 16Y99, 03F55, 03G25
References:
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