scholarly journals Proper Fuzzification of Prime Ideals of a Hemiring

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
H. V. Kumbhojkar
Keyword(s):  
Prime Ideals ◽  
Different Types ◽  
Fuzzy Ideal ◽  
Nil Radical

Prime fuzzy ideals, prime fuzzyk-ideals, and prime fuzzyh-ideals are roped in one condition. It is shown that this way better fuzzification is achieved. Other major results of the paper are: every fuzzy ideal (resp.,k-ideal,h-ideal) is contained in a prime fuzzy ideal (resp.,k-ideal,h-ideal). Prime radicals and nil radicals of a fuzzy ideal are defined; their relationship is established. The nil radical of a fuzzyk-ideal (resp., anh-ideal) is proved to be a fuzzyk-ideal (resp.,h-ideal). The correspondence theorems for different types of fuzzy ideals of hemirings are established. The concept of primary fuzzy ideal is introduced. Minimum imperative for proper fuzzification is suggested and it is shown that the fuzzifications introduced in this paper are proper fuzzifications.

scholarly journals Fuzzy Prime Ideal Theorem in Residuated Lattices

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Pierre Carole Kengne ◽  
Blaise Blériot Koguep ◽  
Celestin Lele
Keyword(s):  
Prime Ideal ◽  
Maximal Ideal ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Prime Ideals ◽  
Fuzzy Subset ◽  
Different Types ◽  
Fuzzy Ideal ◽  
Prime Ideal Theorem

This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization. Also, we introduce different types of fuzzy prime ideals and establish existing relationships between them. We prove that any fuzzy maximal ideal is a fuzzy prime ideal in residuated lattice. Finally, we give and prove the fuzzy prime ideal theorem in residuated lattice.

Nil radical of fuzzy ideal

1992 ◽  
Vol 47 (1) ◽  
pp. 117-120 ◽  
Author(s):  
F.I. Sidky ◽  
S.A. Khatab
Keyword(s):  
Fuzzy Ideal ◽  
Nil Radical

scholarly journals Rough semigroups and rough fuzzy semigroups based on fuzzy ideals

2016 ◽  
Vol 14 (1) ◽  
pp. 1114-1121 ◽  
Author(s):  
Qiumei Wang ◽  
Jianming Zhan
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Congruence Relation ◽  
Prime Ideals ◽  
Fuzzy Ideal ◽  
Lower And Upper Approximations ◽  
Special Congruence

AbstractIn this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.

FUZZY PRIME IDEALS OF A SEMIRING AND FUZZY PRIME SUB-SEMIMODULES OF A SEMIMODULE OVER A SEMIRING

2006 ◽  
Vol 02 (03) ◽  
pp. 219-236 ◽  
Author(s):  
J. AHSAN ◽  
K. SAIFULLAH ◽  
M. SHABIR
Keyword(s):  
Prime Ideals ◽  
Fuzzy Ideal

In this paper we define fuzzy prime right ideals and fuzzy prime subsemimodules of a right R-semimodule. We characterize those semirings for which each fuzzy ideal is prime and those semirings for which each fuzzy right ideal is prime.

scholarly journals On Fuzzy Ideals ofBL-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Biao Long Meng ◽  
Xiao Long Xin
Keyword(s):  
Prime Ideal ◽  
Distributive Lattice ◽  
Fuzzy Set ◽  
Representation Theorem ◽  
Prime Ideals ◽  
Converse Implication ◽  
Fuzzy Ideal ◽  
Stone Representation

In this paper we investigate further properties of fuzzy ideals of aBL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of aBL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime idealωis a fuzzy irreducible ideal if and only ifω0=1and|Im⁡(ω)|=2. We give the Krull-Stone representation theorem of fuzzy ideals inBL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of aBL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.

scholarly journals Prime Fuzzy Bi-Ideals in Near-Subtraction Semigroups

2021 ◽  
Vol 7 ◽  
pp. 29-33
Author(s):  
K. Mumtha ◽  
V. Mahalakshmi ◽  
S. Usha Devi
Keyword(s):  
Prime Ideals ◽  
Fuzzy Ideal ◽  
New Type

A study on fuzzy prime ideals in near-subtraction semigroups is already known. We have to expand the concept of prime fuzzy bi-ideals in near-subtraction semigroups and analyse some of its properties to characterize it. This will lead to learn a new type of fuzzy ideal and to develope the researcher to made their research.

scholarly journals Characterizations of Fuzzy Ideals in Coresiduated Lattices

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Yan Liu ◽  
Mucong Zheng
Keyword(s):  
Prime Ideal ◽  
Prime Ideals ◽  
Fuzzy Ideal

The notions of fuzzy ideals are introduced in coresiduated lattices. The characterizations of fuzzy ideals, fuzzy prime ideals, and fuzzy strong prime ideals in coresiduated lattices are investigated and the relations between ideals and fuzzy ideals are established. Moreover, the equivalence of fuzzy prime ideals and fuzzy strong prime ideals is proved in prelinear coresiduated lattices. Furthermore, the conditions under which a fuzzy prime ideal is derived from a fuzzy ideal are presented in prelinear coresiduated lattices.

scholarly journals Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings

2008 ◽  
Vol 2008 ◽  
pp. 1-8
Author(s):  
E. Hashemi
Keyword(s):  
Laurent Polynomial ◽  
Prime Radical ◽  
Polynomial Rings ◽  
Prime Ideals ◽  
Laurent Polynomials ◽  
Relationship Of ◽  
The Relationship ◽  
Nil Radical

We first study connections betweenα-compatible ideals ofRand related ideals of the skew Laurent polynomials ringR[x,x−1;α], whereαis an automorphism ofR. Also we investigate the relationship ofP(R)andNr(R)ofRwith the prime radical and the upper nil radical of the skew Laurent polynomial rings. Then by using Jordan's ring, we extend above results to the case whereαis not surjective.

The nil radical of a fuzzy ideal

1993 ◽  
Vol 59 (1) ◽  
pp. 87-93 ◽  
Author(s):  
K.C. Gupta ◽  
Manoj K. Kantroo
Keyword(s):  
Fuzzy Ideal ◽  
Nil Radical
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