An integral domain $D$ is called a emph{locally GCD domain} if $D_{M}$ is aGCD domain for every maximal ideal $M$ of $D$. We study somering-theoretic properties of locally GCD domains. E.g., we show that $%D$ is a locally GCD domain if and only if $aDcap bD$ is locally principalfor all $0neq a,bin D$, and flat overrings of a locally GCD domain arelocally GCD. We also show that the t-class group...

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ simultaneously P$v$MDs (resp., Krull, G-GCD, Noetherian, Strong Mori). A complete characterization when a pullback is P$v$MD GCD, Mori, Mori) given. As corollaries, investigate...

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).

Let K be a locally compact hypergroup. In this paper we initiate the concept of fundamental domain in locally compact hypergroups and then we introduce the Borel section mapping. In fact, a fundamental domain is a subset of a hypergroup K including a unique element from each cosets, and the Borel section mapping is a function which corresponds to any coset, the related unique element in the fun...

On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in Q( √ d) where d ∈ {−2,−7,−11,−19}. Thus a binary gcd like algorithm is presented for a unique factorization domain which is not Euclidean (case d = −19). Together with the earlier known binary gcd like algorithms for the ring of integers in Q( √−1) and Q(√−3...

An integral domain without irreducible elements is called an antimatter domain. We give some monoid domain constructions of antimatter domains. Among other things, we show that if D is a GCD domain with quotient …eld K that is algebraically closed, real closed, or perfect of characteristic p > 0, then the monoid domain D[X;Q+] is an antimatter GCD domain. We also show that a GCD domain D is ant...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.

The stress-activated protein kinase Gcn2 regulates protein synthesis by phosphorylation of translation initiation factor eIF2α, from yeast to mammals. The Gcn2 kinase domain (KD) is inherently inactive and requires allosteric stimulation by adjoining regulatory domains. Gcn2 contains a pseudokinase domain (YKD) required for high-level eIF2α phosphorylation in amino acid starved yeast cells; how...

Let Γ be a finite group and K a number field. We show that the operation ψk defined by Cassou-Noguès and Taylor on the locally free classgroup Cl(OKΓ ) is a symmetric power operation if gcd(k, ord(Γ )) = 1. Using the equivariant Adams-Riemann-Roch theorem, we furthermore give a geometric interpretation of a formula established by Burns and Chinburg for these operations.

This paper considers the computation of greatest common divisor (GCD) dt1,t2(x,y) three bivariate Bernstein polynomials that are defined in a rectangular domain, where t1(t2) is degree when it written as polynomial x(y) whose coefficients y(x). The Sylvester resultant matrix and its subresultant matrices used for degrees GCD. It shown there four forms these they differ their computational prope...