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Fuzzy ideals of artinian rings
Fuzzy Sets and Systems, 1990Main result: A ring R with unity is Artinian iff every of its fuzzy ideals I: \(R\to [0,1]\) is finitely valued. The author discusses also a few related results of \textit{T. K. Mukherjee}, \textit{M. K. Sen} [ibid. 21, 99-104 (1987; Zbl 0617.13001)] and \textit{F. Z. Pan} [ibid. 21, 105-113 (1987; Zbl 0616.16013)].
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Fuzzy Sets and Systems, 1998
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Fuzzy ideals and fuzzy semiprime ideals: Some ring theoretic analogues
Information Sciences, 1992The author contributes to the straightforward fuzzification of the concept ideal in a ring. Some interesting analogues of the classical results are obtained: -- The fuzzy nil radical of the \(n\)th power of a fuzzy prime ideal equals itself. -- Under rather general supplementary conditions it is shown that a fuzzy ideal of a ring is fuzzy primary if ...
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1995
The authors define a fuzzy ring. The approach is similar to the one used by the first author [in Inf. Sci. 80, No. 3-4, 253-282 (1994; Zbl 0832.20088)] to define a fuzzy group. The authors define and examine the notions of a fuzzy subring and a fuzzy ideal.
Dib, K. A., Galhum, N., Hassan, A. A. M.
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The authors define a fuzzy ring. The approach is similar to the one used by the first author [in Inf. Sci. 80, No. 3-4, 253-282 (1994; Zbl 0832.20088)] to define a fuzzy group. The authors define and examine the notions of a fuzzy subring and a fuzzy ideal.
Dib, K. A., Galhum, N., Hassan, A. A. M.
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JP Journal of Algebra, Number Theory and Applications, 2017
Summary: The origin of the present study is the paper [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)], where the author studied the concept of 2-absorbing ideals in commutative rings. Many classical theorems on ideals have been used to arrive at the results.
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Summary: The origin of the present study is the paper [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)], where the author studied the concept of 2-absorbing ideals in commutative rings. Many classical theorems on ideals have been used to arrive at the results.
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2018
Fuzzy set theory was first propounded by Zadeh in 1965. Subsequently, Rosenfeld did pioneering work by applying fuzzy sets to the realm of group theory and formulated the concept of a fuzzy subgroup of a group with respect to the t-norm Minimum. Since then, a host of mathematicians have been engrossed in extending the concepts and results of abstract ...
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Fuzzy set theory was first propounded by Zadeh in 1965. Subsequently, Rosenfeld did pioneering work by applying fuzzy sets to the realm of group theory and formulated the concept of a fuzzy subgroup of a group with respect to the t-norm Minimum. Since then, a host of mathematicians have been engrossed in extending the concepts and results of abstract ...
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