[PDF] Top 20 On ordered hypersemigroups with idempotent ideals, prime and weakly prime ideals

... on ordered semigroups are examined in case of ordered hyper- ...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 ... See full document

... of ordered semihypergroups in ...of weakly semiprime and irreducible hyperideals in ordered semihypergroups, and moreover establish the relationship between the five classes of ...semisimple ... See full document

... fuzzy prime if and only if it is semisim- ple and its set of fuzzy ideals is totally ...fuzzy prime right ideals of a semigroup and we prove that if the set of all fuzzy right ideals of ... See full document

... partially ordered set (X , ≤) is called a meet semi lattice if a ∧ b (=glb{a, b}) exists for all a and b ∈ X ...and idempotent and satisfying the absorption laws, namely a ∧ (a ∨ b) = a = a ∨ (a ∧ b) for ... See full document

... Proof: Suppose each i-v fuzzy bi-ideal of N is idempotent. Let λ be a arbitrary i-v fuzzy bi-ideal and µ ν , be an i-v fuzzy bi-ideals of N such that µ ν λ ≤ . Since the set of i-v fuzzy bi-ideals of ... See full document

... are weakly primary ideals but not weakly prime and K = {0, a, b, c} is prime and hence weakly primary because every prime ideal is weakly ...these ideals are ... See full document

... 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 ... See full document

... all ideals containing a and is the set of all finite sum of elements of the form na + xαa + aβy + uγaµv, where n is an integer, x, y, u, v are elements of M and α, β, γ, µ are elements of ... See full document

... 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 ... See full document

... The concept of an ideal was introduced in an ADL analogous to that in a distributive lattice [3]. If R is an ADL, then the set P I (R) of all principal ideals of R form a distributive lattice. This enables to ... See full document

... 3. Primary decomposition. In this section, we describe a method of decom- posing a fuzzy ideal as an intersection of primary fuzzy ideals. Assuming the existence of such a decomposition, we prove some uniqueness ... See full document

... Theorem 3.1. Let R be a prime ring and I a nonzero left ideal of R. Suppose that R admits a generalized derivation F with associated derivation d of R such that d(Z(R)) 6= 0. Further, if R satisfies the condition ... See full document

... an ordered semigroup is a semigroup together with a partial order that is compatible with the semigroup ...operation. Ordered semigroups have many applications in the theory of sequential machines, formal ... See full document

... distinct prime 0-ideals of a nearlattice ⇒ ! and # be two distinct minimal prime 0-ideals of ...a prime ideal, ∉ ! and ∉ ! ⇒ ∧ ∉ ... See full document

... completely prime ideal (briefly, UAC) (resp. a lower approximation completely prime ideal (briefly, LAC) and a rough completely prime ideal (briefly, RC)) are ... See full document

... The structure of the ideals, in particular the prime ideals, of Frechet and Banach algebras is examined and we show that no infinite dimensional separable Banach algebra can be a locally[r] ... See full document

... 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 ... See full document

... 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 ... See full document

... 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 ... See full document

... the prime, strongly prime, semiprime and irreducible fuzzy bi-ideals of ...fuzzy ideals and fuzzy filters of ordered ternary ... See full document