minimal prime ideals
Weakly Prime and Weakly Primary Ideals in Gamma Seminearrings
... smallest prime ideal and all other prime ideals are idempotent and are linearly ...a prime ideal. And in such case there exist two nonzero minimal prime ideals J 1 and J 2 ...
9
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
Ore Extensions over Weak (Sigma)-rigid Rings and (sigma(*))-rings
... of prime ideals of R is denoted by Spec(R). The set of minimal prime ideals of R is denoted by M ...The prime radical and the set of nilpotent elements of R are denoted by P(R) ...
9
0-ideals in 0-distributive Nearlattice
... algebra, ideals play a vital role in nearlattices. Special types of ideals are introduced and studied in Nearlattices by various authors (See ...the minimal prime ideals containing ...
9
Decomposable and Strongly Decomposable Nearlattices
... of minimal prime ideals in S. For a prime ideal ! in S define C = ⋂ {D∈% ...two prime ideals to be comparable in a decomposable nearlattice is proved in the following ...
5
Semi Prime Ideals in Meet Semilattices
... semi prime ideals was given by ...semi prime ideal if for all x , y , z ∈ L , x ∧ y ∈ I and x ∧ z ∈ I imply x ∧ ( y ∨ z ) ∈ I ...these ideals in directed above meet semi lattices and provided ...
9
Vol 5, No 4 (2014)
... every prime ideal in L is ...their prime ideals and minimal prime ideals with hull-kernel topology and dual hull-kernel ...
6
π-Modules
... many minimal prime ideals and so M contains only finitely many minimal prime ...quasi-principal prime ideals of rank less than or equal to ...
12
Projective prime ideals and localisation in pi rings
... Let N be the nilpotent radical of R. We prove the result by induction on K, the index of nilpotency of N. The case k l 1 is trivial by the above. Now assume that k 2. Suppose that M is not idempotent. Because M R is ...
13
Vol 7, No 5 (2016)
... The theory of ternary algebraic system was introduced by D.H. Lehmer in 1932 but earlier such structures were studied by Kasner in1904, who gave the idea of n-ary algebras. Ternary semigroups are universal algebras with ...
6
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
Characterization of Prime Ideals in (Z+,<=D)
... In fact, for any mapping C : Z + −→ P (Z + ) such that each member of C (n) is a divisor of n, ≤ C is a partial order on Z + if and only if C is a convolution, as defined above [1, 4]. Definition 3. Let C be a ...
11
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 ...
11
ON FUZZY PRIME AND FUZZY SEMIPRIME IDEALS OF {HYPERGROUPOIDS
... Abstract. We deal with an hypergroupoid endowed with a rela- tion denoted by “≤”, we call it ≤–hypergroupoid. We prove that a nonempty subset A of a ≤–hypergroupoid H is a prime (resp. semiprime) ideal of H if and ...
7
On Ideals and Commutativity of Prime Rings with Generalized Derivations
... the ideals in prime rings as well as the commutativity of prime rings that consider derivations and generalized derivations, see for example [2], [3], [5] and ...free prime ring with center ...
11
FUZZY WEAKLY PRIME -IDEALS IN -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, partial weakly prime Γ-ideal and semiprime ...
13
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 ...
6
A note on maximal non-prime ideals
... prime ideal of R and (ii) If A is any proper ideal of R such that A contains I properly, then A is a prime ideal of R. Similarly, we can define the concept of a maximal non-maximal (respectively, a maximal ...
11
Homomorphisms and L-Fuzzy Ideals in Universal Algebras
... Proof: The above two theorems confirm that @ ↦ ℎ(@) is an onto map from the set of all ℎ -invariant fuzzy prime ideals of to the set of all fuzzy prime ideals of ] . It remains to show that it ...
12
Glivenko Congruence on a Nearlattice Related to Semi Prime Ideals
... F . Hence by ( ii ) , there exists a prime filter Q ⊇ F such that Q ∩ A ⊥ = φ . Then b ∨ c ∉ S − Q . This implies either b ∉ S − Q or c ∉ S − Q as S − Q is a prime ideal. Hence either b ∈ Q or c ∈ Q . ...
7