Results 231 to 240 of about 17,500 (266)
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2003
In this chapter, we characterize prime fuzzy ideals of a semigroup S. Sections 7.1–7.11 are essentially from [151]. We show that a nonconstant fuzzy ideal f of a semigroup S is prime if and only if f is two-valued and there exists an element x0 in S such that f(x0) = 1 and f1 = {x ∈ S | f(x) = 1} is a prime ideal of S.
John N. Mordeson +2 more
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In this chapter, we characterize prime fuzzy ideals of a semigroup S. Sections 7.1–7.11 are essentially from [151]. We show that a nonconstant fuzzy ideal f of a semigroup S is prime if and only if f is two-valued and there exists an element x0 in S such that f(x0) = 1 and f1 = {x ∈ S | f(x) = 1} is a prime ideal of S.
John N. Mordeson +2 more
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Interval-valued prime fuzzy ideals of semigroups
Lobachevskii Journal of Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kar, S., Shum, K. P., Sarkar, P.
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Fuzzy prime ideals and fuzzy radical ideals
Information Sciences, 1990Abstract Some properties of the fuzzy prime ideals and radical ideals are studied. Also we study the structure of fuzzy principal ideals.
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Prime L-fuzzy ideals and primary L-fuzzy ideals
Fuzzy Sets and Systems, 1988The author introduces the concepts of a primary L-fuzzy ideal and a primary L-fuzzy ideal belonging to a prime L-fuzzy ideal where L is a complete distributive lattice. Let A be an L-fuzzy ideal of a ring X and \(X_ A=\{x\in X| A(x)=A(0)\}\). A is called prime if for \(a,b\in X\), \(A(ab)=A(0)\) implies \(A(a)=A(0)\) or \(A(b)=A(0)\).
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Prime Fuzzy Ideals, Completely Prime Fuzzy Ideals of Po-$$\Gamma $$-Semigroups Based on Fuzzy Points
2015Using fuzzy points the notions of prime fuzzy ideals, weakly prime fuzzy ideals, completely prime fuzzy ideals, and weakly completely prime fuzzy ideals of a po-\(\Gamma \)-semigroup have been introduced. Some important properties and characterizations of these ideals have been obtained.
Pavel Pal +2 more
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Equiprime, 3-prime and c-prime fuzzy ideals of nearrings
Soft Computing, 2008The notion of primeness for fuzzy ideals of near-rings is not new, but the approach of the authors to this topic is in the sense that they deal with fuzzy ideals with thresholds. This opens up more possibilities and leads to a wider and more interesting class of examples.
Kedukodi, Babushri Srinivas +2 more
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Fuzzy Sets and Systems, 1990
Abstract This paper characterizes all fuzzy prime ideals P of an arbitrary ring R. We show that a nonconstant fuzzy ideal P of R is prime if and only if P0 ={;x ϵ R: P(x) = P(0)}; is a prime ideal of R, P is two-valued, and P(0) = 1. Examples are given showing that P0 is a prime ideal is not sufficient for P to be a fuzzy prime ideal and that P0 may ...
A.S. Malik, John N. Mordeson
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Abstract This paper characterizes all fuzzy prime ideals P of an arbitrary ring R. We show that a nonconstant fuzzy ideal P of R is prime if and only if P0 ={;x ϵ R: P(x) = P(0)}; is a prime ideal of R, P is two-valued, and P(0) = 1. Examples are given showing that P0 is a prime ideal is not sufficient for P to be a fuzzy prime ideal and that P0 may ...
A.S. Malik, John N. Mordeson
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Spectrum of prime fuzzy ideals
Fuzzy Sets and Systems, 1994An attempt has been made to introduce an appropriate topology on the set of prime fuzzy ideals. Instead of appealing to other definitions of prime fuzzy ideals, as in literature, the author has taken his own definition introduced earlier; such prime fuzzy ideals in a commutative ring \(R\) with identity are denoted by \(F \text{spec} (R)\); the author ...
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A characterization of L-fuzzy prime ideals
Fuzzy Sets and Systems, 1991A definition is given for the concept of an \(L\)-fuzzy prime ideal that is more restrictive than the concept introduced by \textit{Y. Zhang} [ibid. 27, 345-350 (1988; Zbl 0663.13001)]. The new definition is based on the concept of an \(L\)-fuzzy point, where even the value zero is allowed, which means that the \(L\)-fuzzy set \(\phi: X\to \{0\}\) is ...
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Fuzzy rough prime and semi-prime ideals in semigroups
AIP Conference Proceedings, 2019The purpose of this paper is to introduce the concept of fuzzy rough prime ideals and fuzzy rough semi-prime ideals in semigroups. Some results based on fuzzy rough prime and fuzzy rough semi-prime ideals are established.The purpose of this paper is to introduce the concept of fuzzy rough prime ideals and fuzzy rough semi-prime ideals in semigroups ...
V. S. Subha +2 more
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