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Residual Quotient and Annihilator of Intuitionistic Fuzzy Sets of Ring and Module


Affiliations
1 P.G. Department of Mathematics, D.A.V. College, Jalandhar City, Punjab, India
2 IKG PT University, Jalandhar , Punjab, India
 

In this paper, we introduce the concept of residual quotient of intuitionistic fuzzy subsets of ring and module and then define the notion of residual quotient intuitionistic fuzzy submodules , residual quotient intuitionistic fuzzy ideals. We study many properties of residual quotient relating to union, intersection, sum of intuitionistic fuzzy submodules (ideals). Using the concept of residual quotient, we investigate some important characterization of intuitionistic fuzzy annihilator of subsets of ring and module. We also study intuitionistic fuzzy prime submodules with the help of intuitionistic fuzzy annihilators. Many related properties are defined and discussed.

Keywords

Intuitionistic Fuzzy (prime) Submodule (ideal), Residual Quotient Intuitionistic Fuzzy Submodules (ideal), Intuitionistic Fuzzy Annihilator, Semiprime Ring.
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  • Residual Quotient and Annihilator of Intuitionistic Fuzzy Sets of Ring and Module

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Authors

P. K. Sharma
P.G. Department of Mathematics, D.A.V. College, Jalandhar City, Punjab, India
Gagandeep Kaur
IKG PT University, Jalandhar , Punjab, India

Abstract


In this paper, we introduce the concept of residual quotient of intuitionistic fuzzy subsets of ring and module and then define the notion of residual quotient intuitionistic fuzzy submodules , residual quotient intuitionistic fuzzy ideals. We study many properties of residual quotient relating to union, intersection, sum of intuitionistic fuzzy submodules (ideals). Using the concept of residual quotient, we investigate some important characterization of intuitionistic fuzzy annihilator of subsets of ring and module. We also study intuitionistic fuzzy prime submodules with the help of intuitionistic fuzzy annihilators. Many related properties are defined and discussed.

Keywords


Intuitionistic Fuzzy (prime) Submodule (ideal), Residual Quotient Intuitionistic Fuzzy Submodules (ideal), Intuitionistic Fuzzy Annihilator, Semiprime Ring.

References