On intuitionistic fuzzy prime submodules

In this paper, we explore the decomposition of intuitionistic fuzzy submodule as the intersection of finite many intuitionistic fuzzy prime submodules. Many other forms of decomposition like irredundant and normal decomposition are also investigated.

Notes on Intuitionistic Fuzzy Sets, 2023

The aim of this paper is to present some characterizations of almost prime ideals and almost prime submodules in the intuitionistic fuzzy environment. We investigate various properties of these concepts and achieve many results.

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.

Notes on Intuitionistic Fuzzy Sets, 2023

Let L be a complete lattice. We introduce and characterise intuitionistic L-fuzzy classical prime submodule and intuitionistic L-fuzzy 2-absorbing submodules of a unitary module M over a commutative ring R with identity. We compare both of these submodules with intuitionistic L-fuzzy prime submodules. It is proven that in the case of the multiplication module M , the two notions of intuitionistic L-fuzzy classical prime submodules and intuitionistic L-fuzzy prime submodules coincide. Many other related results concerning these notions are obtained.

7th Int. IFS and Contemporary Mathematics Conference at Turkey, 2021

In this talk, we study the concept of residual quotient of IF subsets of ring and module and develop many properties out of these. Using the concept of residual quotient, we investigate some important characterization of annihilator of IF submodules, IF prime(primary) submodules and IF prime(primary) decomposition.

Malaya Journal of Matematik, 2020

In the present manuscript, we introduce and study the notion of primary submodules as well as P-primary submodules of a module in the intuitionistic L-fuzzy environment. Apart from investigating basic properties of these submodules, we explore some foundational results analogous to corresponding submodules. A suitable characterization of intuitionistic L-fuzzy primary (P-primary) submodules in terms of primary (P-primary) submodules are presented.

researchgate.net

The Author has introduced the notion of intuitionistic anti-fuzzy subring and ideal in a ring and studied their properties in . In this paper, the notion of intuitionistic anti-fuzzy submodule of a module is introduced and some of their properties has been discussed.

In this paper, we introduce the concept of intuitionistic fuzzy small submodule with respect to an arbitrary intuitionistic fuzzy submodule of an R-module M. We derive the condition when an intuitionistic fuzzy submodule to be a small submodule with respect to another intuitionistic fuzzy submodule with the crisp small submodule of the R-module M. It is also shown that the sum of two intuitionistic fuzzy small submodules with respect to a fixed intuitionistic fuzzy submodule is again an intuitionistic fuzzy submodule with respect to the same fixed intuitionistic fuzzy submodule. This result can be extended to an arbitrary sum of intuitionistic fuzzy submodules. Further, we prove that the homomorphic image of an intuitionistic fuzzy small submodule with respect to a fixed intuitionistic fuzzy submodule is again an intuitionistic fuzzy small submodule with respect the homomorphic image of the fixed intuitionistic fuzzy submodule.

Information Sciences, 2006

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to H v -modules. The notion of an intuitionistic fuzzy H v -submodule of an H vmodule is introduced, and some related properties are investigated. Characterizations of intuitionistic fuzzy H v -submodules are given.

Malaya Journal of Matematik, 2020

This article is in continuation to author's previous paper, on intuitionistic L-fuzzy primary and P-primary submodules,