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Issue:Group action on intuitionistic fuzzy ideals of Γ-ring

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http://ifigenia.org/wiki/issue:nifs/31/2/139-153
Title of paper: Group action on intuitionistic fuzzy ideals of Γ-ring
Author(s):
Poonam Kumar Sharma     0000-0001-5463-8665
P. G. Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 2, pages 139–153
DOI: https://doi.org/10.7546/nifs.2025.31.2.139-153
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Abstract: Group actions serve as a powerful tool for exploring the symmetry and automorphism properties of rings. In this paper, we examine group actions on intuitionistic fuzzy ideals (IFIs) within a Γ-ring [math]\displaystyle{ \mathcal{M} }[/math]. We introduce the concept of the intrinsic product of IFIs in [math]\displaystyle{ \mathcal{M} }[/math] and explore various properties of intuitionistic fuzzy prime ideals under the influence of group actions. Further, we propose the notion of an intuitionistic fuzzy [math]\displaystyle{ \mathcal{G} }[/math]-prime ideal in [math]\displaystyle{ \mathcal{M} }[/math]. We demonstrate that for an IFI [math]\displaystyle{ A }[/math] of [math]\displaystyle{ \mathcal{M} }[/math], the ideal [math]\displaystyle{ A^{\mathcal{G}} = \bigcap_{g\in \mathcal{G}}A^{g} }[/math] represents the largest [math]\displaystyle{ \mathcal{G} }[/math]-invariant IFI contained within [math]\displaystyle{ A }[/math]. Additionally, we establish that the [math]\displaystyle{ \mathcal{G} }[/math]-primeness of [math]\displaystyle{ A^{\mathcal{G}} }[/math] is uniquely characterized by the [math]\displaystyle{ \mathcal{G} }[/math]-primeness of [math]\displaystyle{ A }[/math]. Lastly, we examine the behavior of intuitionistic fuzzy [math]\displaystyle{ \mathcal{G} }[/math]-prime ideals of [math]\displaystyle{ \mathcal{M} }[/math] under a [math]\displaystyle{ \mathcal{G} }[/math]-homomorphism.
Keywords: Γ-ring, Intuitionistic fuzzy prime ideal, [math]\displaystyle{ \mathcal{G} }[/math]-invariant intuitionistic fuzzy ideals, [math]\displaystyle{ \mathcal{G} }[/math]-prime intuitionistic fuzzy ideals, [math]\displaystyle{ \mathcal{G} }[/math]-homomorphism.
AMS Classification: 03F55, 13A15, 13A50; 16W22, 16Y80.
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