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.

Let R be a ring, σ an injective endomorphism of R and δ a σderivation of R. We prove that if R is semiprime left Goldie then the same holds for the Ore extension R[x;σ, δ] and both rings have the same left uniform dimension.

The purpose of this paper is to prove the following result: Let R be a 2torsion free semiprime ring and let T : R → R be an additive mapping, such that 2T (x) = T (x)x + xT (x) holds for all x ∈ R. In this case T is left and right centralizer.

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

In this paper, we introduce (α, α)-symmetric derivations and establish some interesting results and also extend an important result of J. Vukman by using (α, α)-derivation.

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

In a commutative f-ring, an 1-ideal I is called pseudoprime if ab = 0 implies a E I or b E I, and is called square dominated if for every a E I, lal < x2 for some x E A such that x2 E I. Several characterizations of pseudoprime 1-ideals are given in the class of commutative semiprime frings in which minimal prime 1-ideals are square dominated. It is shown that the hypothesis imposed on the f-ri...