Maximal and Prime Ideals
A note on maximal non-prime ideals
... a maximal non- P , if R does not have P , whereas each subring S of T with R ⊂ S has property P ...of maximal non-Noetherian subring of a ring T was investigated in ...on maximal non-P subring of a ...
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Factoring of Prime Ideals in Extensions
... We will fill in the gap at the end of the proof of the ram-rel identity. Let S be a mul- tiplicative subset of the integral domain A, and let M be a maximal ideal of A disjoint from S. Consider the composite map A ...
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On Semi Prime Ideals in Nearlattices
... Semi prime ideals in a general lattice by generalizing the notion of 0-distributive ...these ideals in a general nearlattice and include some of their ...regarding maximal filters and include ...
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Prime O-ideals of distributive lattices
... a prime ideal of a distributive lattice to become an O ...between prime O-ideals and minimal prime ideals of a distributive ...distinct prime O-ideals of a distributive ...
Semi Prime Ideals in Meet Semilattices
... D = ∧ .Hence D is a filter disjoint from J. Then by Lemma 4, there is a maximal filter M ⊇ D but disjoint form J .Then by Lemma 2, S-M is minimal prime down set containing J. Now x ∉ S − M as x ∈ D implies ...
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Projective prime ideals and localisation in pi rings
... a maximal ideal. Extending the result to a general prime ideal presents a technical ...the prime ideal being examined extends to a prime ideal which belongs to a localisable clique in a ...
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Some Properties of Semi-Prime Ideals in Lattices
... a maximal filter if for any filter M ⊇ F implies either M = F or M = L ...a prime ideal (down set) if for a , b ∈ L , a ∧ b ∈ I imply either a ∈ I or b ∈ I ...A prime ideal P is called a minimal ...
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Γ-Semigroups in which Prime Γ-Ideals are Maximal
... proper prime Γ–ideals, by theorem ...proper prime Γ-ideals, we have √ <a> = √<b> = ...unique prime Γ-ideal P such that S is a 0-simple extension of the Archimedian Γ–sub ...
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F-thresholds and generalized test ideals of determinantal ideals of maximal minors
... multiplier ideals in characteristic zero, ...test ideals as their prime characteristic analogue, ...multiplier ideals are defined geometrically, using log resolutions (see [Laz]), or even ...
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Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings
... Theorem 1. Let M be an m-system of a Γ-seminearring R whose each ideal is a subtrac- tive. Let I be an ideal with I ∩ M = ∅. Then, there exists a weakly prime ideal P such that I ⊆ P and P ∩ M = ∅. Proof. Let = = ...
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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 ...
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Prime Ideals and Strongly Prime Ideals of Skew Laurent Polynomial Rings
... α-compatible ideals of R and related ideals of the skew Laurent polynomials ring Rx, x −1 ; α, where α is an automorphism of ...the prime radical and the upper nil radical of the skew Laurent ...
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I-prime ideals
... weakly prime ideals called ...I-prime ideals and study some of its ...I-prime ideals becomes prime or weakly prime and we construct the view of I-prime ideal ...
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Fuzzy prime ideals redefined
... )-fuzzy prime and fuzzy primary ideal There are several deferent definitions of a fuzzy prime ideal and a fuzzy primary ideal of ...a prime ideal S of R, we mean an ideal of R such that ab ∈ S = ⇒ a ∈ ...
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Rough Semi Prime Ideals and Rough Bi-Ideals in Rings
... In this paper, we shall introduce the concept of rough semi-prime ideal, rough bi-ideal and give some properties of anti-homomorphism on these rough ideals. Key words: rough ring, rough ideal, rough ...
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Characterization of Prime Ideals in (Z+,<=D)
... It is well known that Z + has the structure of a distributive lattice with respect to the division order. The division ordering is precisely the partial ordering ≤ D induced by the Dirichlet’s convolution D. In this ...
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FUZZY WEAKLY PRIME -IDEALS IN -RINGS
... WEAKLY PRIME Γ-IDEALS IN Γ-RINGS ...weakly prime Γ-ideal, fuzzy partial weakly prime Γ-ideal and fuzzy semiprime Γ- ideal of a commutative Γ-ring with nonzero ...weakly prime Γ-ideal, ...
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INTUITIONISTIC FUZZY WEAKLY PRIME IDEALS
... WEAKLY PRIME IDEALS TU ˘ GBA ARKAN*, SERKAN ONAR, DENIZ S ¨ ONMEZ, BAYRAM ALI ERSOY ...fuzzy ideals of commutative ring R with identity have been given as pre- ...weakly prime ideals, ...
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Fuzzy Prime Ideals And Filters Of Lattices
... L-fuzzy ideals of general ...L-fuzzy ideals of bounded distributive ...the prime L-fuzzy ideals and filters and obtain a one-to-one correspondence between the prime L-fuzzy ...
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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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