We reduce the problem of factoring a semiprime integer to the problem of (numerically) integrating a certain highly oscillatory function. We provide two algorithms to address this problem, one based on the residue theorem and the other in the (extended) Cauchy’s argument principle. In the former algorithm, we show that computing the residue of the function at a certain pole leads to obtaining t...

In this paper, we discuss some basic properties of rough intuitionistic fuzzy set in semigroup. Intuitionistic fuzzy analogues of some results concerning rough semiprime (semiprimary) ideals in semigroup are obtained. 2010 AMS Classification: 03E72, 03F55, 06B10.

It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...

We establish a necessary condition for a commutative Banach algebra A so that there exists a homomorphism θ from A into another Banach algebra such that the prime radical of the continuity ideal of θ is not a finite intersection of prime ideals in A. We prove that the prime radical of the continuity ideal of an epimorphism from A onto another Banach algebra (or of a derivation from A into a Ban...

The separating space of a derivation onA is a separating ideal [2, Chapter 5]; it also satisfies the same property for the left products. The following assertions are of the most famous conjectures about derivations on Banach algebras: (C1) every derivation on a Banach algebra has a nilpotent separating ideal; (C2) every derivation on a semiprime Banach algebra is continuous; (C3) every derivat...

In this paper we introduce the notion of interval-valued (i.v.) fuzzy prime and semiprime ideals of a hypersemiring and study different properties of these two ideals. Finally, we examine the strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a hypersemiring and characterize the equivalence of primeness, strongly irreducibility and irreducibility of an i.v. fuzzy ideal of a fu...

In this paper we investgate some properties of fuzzy ideal extension of fuzzy ideal, fuzzy prime ideal, fuzzy semiprime ideal of a Γ−semiring. Among other results we have obtained a characterization of a prime ideal I of a Γ−semiring in terms of fuzzy ideal extension of its characteristic function λI . Mathematics Subject Classification[2000]:16Y60, 16Y99, 03E72

Preface The term " quantum group " was popularized by Drinfeld in his address to the International Congress of Mathematicians in Berkeley. However, the concepts of quantum groups and quasitriangular Hopf algebras are the same. Therefore, Hopf algebras have close connections with various areas of mathematics and physics. The development of Hopf algebras can be divided into five stages. The first...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...