• East Asian mathematical journal
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• 제27권1호
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• pp.75-82
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• 2011

In this paper, we will introduce the concept of fuzzy mulitplication module. We will define a new operation called a product on th family of all fuzzy submodules of a fuzzy mulitplication module. We will define a fuzzy subset of the idealization ring R+M and find some relations with the product of fuzzy submodules and product of fuzzy ideals of the idealization ring R+M. Some properties of weakly fuzzy prime submoduels and fuzzy prime submodules which are de ned by T.K.Mukherjee M.K.Sen and D.Roy will be introduced. We will investigate some properties of fuzzy prime submodules of a fuzzy multiplication module.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.445-460
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• 2022

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.

• 한국지능시스템학회논문지
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• 제20권5호
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• pp.734-740
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• 2010

We define and study the fuzzy nil radical of a fuzzy ideal of a commutative $\kappa$-semiring.

• East Asian mathematical journal
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• 제23권1호
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• 대한수학회보
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• 제35권3호
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• pp.455-464
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• 1998

In this paper, we give another proof of Theorem 2.13 of [4] without using the sup property. For the homomorphic image $f(\mu)$ and preimage $f^{-1}(\nu)$ of fuzzy left (resp. right) ideals $\mu$ and $\nu$ respectively, we establish the chains of level left (resp. right) ideals of $f(\mu)$ and $f^{-1}(\nu)$, respectively. Moreover, we prove that a necessary condition for a fuzzy ideal $\mu$ of a near-ring $R$ to be prime is that $\mu$ is two-valued.

• 한국지능시스템학회논문지
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• 제17권3호
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• pp.423-429
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• 2007

We define and study the fuzzy Jacobson radical of a ${\kappa}$-semiring. Also it is shown that the Jacobson radical of the quotient semiring R/FJR(R) of a ${\kappa}$-semiring by the fuzzy Jacobson radical FJR(R) is semisimple. And the algebraic properties of the fuzzy ideals FJR(R) and FJR(S) under a homomorphism from R onto S are also discussed.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.855-867
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• 2001

This note we give a construction of a quotient ring $R/{\mu}$ induced via a fuzzy ideal ${\mu}$ in a ring R. The Fuzzy First, Second and Third Isomorphism Theorems are established. For some applications of this construction of quotient rings, we show that if ${\mu}$ is a fuzzy ideal of a commutative ring R, then $\mu$ is prime (resp. $R/{\mu}$ is a field, every zero divisor in $R/{\mu}$ is nilpotent). Moreover we give a simpler characterization of fuzzy maximal ideal of a ring.

• East Asian mathematical journal
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• 제9권1호
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• pp.105-111
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• 1993