Prime Ideals
INTUITIONISTIC FUZZY WEAKLY PRIME IDEALS
... fuzzy ideals of commutative ring R with identity have been given as pre- ...weakly prime ideals, intuitionistic fuzzy partial weakly prime ideals, intuitionistic fuzzy weakly semiprime ...
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Reluctant Intuitionistic Anti-Fuzzy Soft Prime Ideals of BCK-Algebras
... commutative ideals and reluctant intuitionistic anti- fuzzy soft prime ideals in BCK-algebras are introduced and related properties are ...soft ideals and reluctant intuitionistic anti- fuzzy ...
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σ-sporadic prime ideals and superficial elements
... Abstract. Let A be a Noetherian ring, I be an ideal of A and σ be a semi-prime operation, different from the identity map on the set of all ideals of A. Results of Essan proved that the sets of associated ...
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Semi-Prime Ideals of Gamma Rings
... The general radical theory for rings had been introduced by Kurosh [4] and Amitsur [1,2]. They studied the generalizations of a general radical. McCoy [5] studied prime and semi-prime ideals and ...
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Semi Prime Ideals in Meet Semilattices
... Remark: By [3] we know that all the conditions of Theorem 10 and Theorem 11 are equivalent in case of lattices. But in meet semi lattices condition (ii)of Theorem 11 does not imply any of the equivalent conditions of ...
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Characterization of Prime Ideals in (Z+,<=D)
... all divisors of n, for any n, then D is called the Dirichlet’s convolution. Corresponding to any general convolution C , we can define a binary relation ≤ C on Z + by “m ≤ C n if and only if m ∈ C (n)”. It is well known ...
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Some Properties of Semi-Prime Ideals in Lattices
... Semi-prime ideals in a general lattice by generalizing the notion of 0-distributive ...Semi-prime ideals. Here we give a simpler proof of a prime Separation theorem in a general lattice ...
10
Associated prime ideals of weak \(\sigma\)-rigid rings and their extensions
... A b s t r a c t . Let R be a right Noetherian ring which is also an algebra over Q (Q the field of rational numbers). Let σ be an automorphism of R and δ a σ-derivation of R. Let further σ be such that aσ(a) ∈ N (R) ...
10
On Semi Prime Ideals in Nearlattices
... semi prime ideals in a ...semi prime ideal if for all x , y , z ∈ L , x ∧ y ∈ I and x ∧ z ∈ I imply x ∧ ( y ∨ z ) ∈ I ...semi prime ideal. Moreover, every prime ideal is semi ...semi ...
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I-prime ideals
... weakly prime ideals and almost prime ideals in mind, we make the following ...weakly prime and n-almost prime ideal is I-prime where I taken to be zero or P n−1 ...
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings
... strongly prime if R is prime with no nonzero nil ...strongly prime if R/P is a strongly prime ring. All strongly prime ideals are taken to be ...(strongly) prime if P is ...
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Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules
... a prime ideal P in a ring R is locally closed if and only if the intersection of all prime ideals properly containing P is also an ideal properly containing ...closed prime ideals is ...
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Fuzzy prime ideals redefined
... The concept of a fuzzy set introduced by Zadeh [] was applied to the group theory by Rosenfeld [] and the ring theory by Liu []. Since then, many scholars have studied the theories of fuzzy subrings and various fuzzy ...
10
Projective prime ideals and localisation in pi rings
... a prime ideal. Clearly P \ I is a left localisable prime ideal of R \ ...localisable prime ideal of R \ ...projective prime ideal of R \ I and so PR P l R P P, the Jacobson radical of R P , is ...
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On Certain Generalized Prime Ideals in Boolean Like Semi ring of Fractions
... Proof. Let P be a semiprime ideal of a Boolean like semiring R such that x 3 ∈ P for some x in R. Then x 2 = (x 3 )(x 3 ) = x 6 = x 2 x 4 = x 2 x 2 = x 2 ∈ P implies x ∈ P (since P is semiprime). Hence P is quasi ...
9
On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals
... The ideals of an ordered hypergroupoid H are idempotent if and only if for any two ideals A and B of H , we have A ∩ B = (A ∗ ...the ideals of H are idempotent if and only if H is semisimple. The ...
13
Some Properties of Fuzzy Soft Prime Ideals
... 3.5. Definition: Let (R, +, .) is a ring and E is a set of parameters and , if [ ] is a set function, where [ ] is the collection of fuzzy subsets of R. Then (I, A) is a fuzzy soft prime ideal on R if and only if ...
5
Glivenko Congruence on a Nearlattice Related to Semi Prime Ideals
... S ′ = . Thus S ′ is a distributive nearlattice with 0 ′ = J . Hence a ′ ∧ b ′ = 0′ , where a ′ = h ( ) a and b ′ = h ( ) b . By hypothesis a ∉ J , b ∉ J , hence a ′ ≠ 0 ′ ≠ b ′ . Choose the ideals A ′ = ( a ′ ∨ b ...
7
FUZZY WEAKLY PRIME -IDEALS IN -RINGS
... If µ(x) ∨ µ(y) = 1, then µ(x) = 1 or µ(y ) = 1 or both are equal to 1. Thus x ∈ I or y ∈ I or both. So x γy ∈ I. Then µ(xγ y) = 1 ≥ µ(x ) and µ(x γy ) = 1 ≥ µ(y ). Therefore µ is a fuzzy prime Γ-ideal. Now we take ...
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A note on maximal non-prime ideals
... Proof. Let a ∈ nil(R), a 6= 0. Let b ∈ M \nil(R). Since nil(R) is a simple R-module, it follows that M(nil(R)) = (0) and so ab = 0. Now a 6= 0 and as b / ∈ nil(R), it follows that b n 6= 0 for all n ≥ 1. This proves that ...
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