Results 141 to 150 of about 47,586 (178)

Prime fuzzy ideals in rings

Fuzzy Sets and Systems, 1989
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Mukherjee, T. K., Sen, M. K.
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Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras

Fuzzy Sets and Systems, 2001
Let \(\mu\) and \(\nu\) be fuzzy ideals of a commutative BCK-algebra \(X\). \(\mu\) is called prime iff it is non-constant and \(\mu(x\wedge y)=\max\{\mu(x), \mu(y)\}\) for all \(x,y\in X\). If \(\nu^+ (x)=1-\inf\{\nu(y) |y\wedge x=0\}\) is a fuzzy ideal of \(X\), then \(\nu\) is called invertible.
Jun, Young Bae, Xin, Xiao Long
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Prime Fuzzy Ideals

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, Davender S. Malik, Nobuaki Kuroki   +2 more
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Interval-valued prime fuzzy ideals of semigroups

Lobachevskii Journal of Mathematics, 2013
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Kar, S., Shum, K. P., Sarkar, P.
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Fuzzy prime ideals and fuzzy radical ideals

Information Sciences, 1990
Abstract 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, 1988
The 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

2015
Using 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, Sujit Kumar Sardar, Rajlaxmi Mukherjee Pal   +2 more
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Equiprime, 3-prime and c-prime fuzzy ideals of nearrings

Soft Computing, 2008
The 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, Kuncham, Syam Prasad, Bhavanari, Satyanarayana   +2 more
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Fuzzy prime ideals of a ring

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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Spectrum of prime fuzzy ideals

Fuzzy Sets and Systems, 1994
An 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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