Quasi-Schreier Domains II

We study a class of integral domains characterized by the property that every nonzero finite intersection of principal ideals is a directed union of invertible ideals.     

拟Z-连续domain和Z-交连续domain

对一般子集系统Z,引入了Rudin性质、拟Z-连续domain及Z-交连续 domain的概念,讨论了它们的基本性质.特别是Z-连续性、拟Z-连续性、 Z-交连 续性和Z-Lawson拓扑之T2性之间的相互关系. 证明了当子集系统Z满足一定条件 时,拟Z-连续domain P上的Z-way below关系Z具有插入性质, P上的Z-Lawson 拓扑λZ(P)是T2的,且P可用Z-Lawson同态嵌入到某方体之中.文中给出了一个 domain P,其上的Lawson拓扑λ(P)是T2的,但P不是拟连续性domain.     

K0-group Transmissibilities of the Tracial Limit of C^＊-algebras

We introduce the tracial limit A = (t4) limn→n∞ (An,pn) and show that if K0(An) has ordered relation, K0(A) has ordered relation naturally. In the case that A is simple and K0(An) is weakly unperforated for every n, K0(A) is weakly unperforated too. Furthermore, the Riesz interpolation property of K0(An) can be transmitted to K0(A).     

Almost Integrally Closed Domains

Abstract

A domain R is called almost integrally closed if R is integrally closed in R _P for each nonzero P ∈ Spec(R). Arbitrary quasilocal domains of (Krull) dimension 1 and arbitrary integrally closed domains are examples of almost integrally closed domains. There are no other examples in the contexts of Noetherian, one-dimensional or pseudo-valuation domains, as a consequence of the fact that any almost integrally closed domain that is not integrally closed has at most one height 1 prime ideal. However, a pullback example shows that a non-integrally closed domain that is almost integrally closed need not be semiquasilocal or of dimension at most 1. By analyzing the behavior of the almost integrally closed property for CPI-extensions, we obtain a characterization of the almost integrally closed locally divided domains. Applications are given to the case of G-domains. It also follows that if a divided domain R is not a field, then R is almost integrally closed if and only if some (resp., each) nonzero P ∈ Spec(R) is such that R _P is almost integrally closed and R is integrally closed in R _P .     

Monoid Domain Constructions of Antimatter Domains

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 field K that is algebraically closed, real closed, or perfect of characteristic p > 0, then the monoid domain D[X; ?⁺] is an antimatter GCD domain. We also show that a GCD domain D is antimatter if and only if P^?1 = D for each maximal t-ideal P of D.     

Polynomial functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X$X$ of reals has the Riesz Interpolation Property if and only if X$X$ is bounded.     

On Pseudo-Almost Valuation Domains

Let R be an integral domain with quotient field K and integral closure R ^′. Anderson and Zafrullah called R an “almost valuation domain” if for every nonzero x ∈ K, there is a positive integer n such that either x ⁿ  ∈ R or x ^?n  ∈ R. In this article, we introduce a new closely related class of integral domains. We define a prime ideal P of R to be a “pseudo-strongly prime ideal” if, whenever x, y ∈ K and xyP ? P, then there is a positive integer m ≥ 1 such that either x ^m  ∈ R or y ^m P ? P. If each prime ideal of R is a pseudo-strongly prime ideal, then R is called a “pseudo-almost valuation domain” (PAVD). We show that the class of valuation domains, the class of pseudo-valuation domains, the class of almost valuation domains, and the class of almost pseudo-valuation domains are properly contained in the class of pseudo-almost valuation domains; also we show that the class of pseudo-almost valuation domains is properly contained in the class of quasilocal domains with linearly ordered prime ideals. Among the properties of PAVDs, we show that an integral domain R is a PAVD if and only if for every nonzero x ∈ K, there is a positive integer n ≥ 1 such that either x ⁿ  ∈ R or ax ^?n  ∈ R for every nonunit a ∈ R. We show that pseudo-almost valuation domains are precisely the pullbacks of almost valuation domains, we characterize pseudo-almost valuation domains of the form D + M, and we use this characterization to construct PAVDs that are not almost valuation domains. We show that if R is a Noetherian PAVD, then R has Krull dimension at most one and R ^′ is a valuation domain; we show that every overring of a PAVD R is a PAVD iff R ^′ is a valuation domain and every integral overring of R is a PAVD.     

Peak Points for Pseudoconvex Domains: A Survey

This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been published elsewhere.      

超越整函数稳定域的某些性质

讨论了有限个超越整函数fi(i=1,2,…,m)迭代生成的函数g=fm°fm-1°…°f1(z)游荡域的性质,在某些条件下,对Brannan和Hayman提出的一个问题给出了肯定的回答.此外,给出了g(z)稳定域有界的一个条件.     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

On Some Elliptic Problems in Unbounded Domains

The author presents a method allowing to obtain existence of a solution for some elliptic problems set in unbounded domains, and shows exponential rate of convergence of the approximate solution toward the solution.     

On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L _2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed.     

Lipschitz Domains,Domains with Corners,and the Hodge Laplacian

ABSTRACT

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of “almost convex” domains, which apply to domains with corners.     

A Note on Property of Cauchy Integral on Classical Domains

In[1],ZhengXueanprovedthat:letRI(n×n)befirstclassicaldomain,Unbecharacteris-ticboundaryofRI,x∈Un,f(x)∈L2(Un).Asz=rx(0≤r<1)→x,Cauchyintegral∫Unf(y)det(I-zy′)-ndyconvergetoafunctioninL2(Un).Inthispaper,wewillfacusourselfonCauchyintegralofL2onclassicaldomains[2]andgetsomeproperties.Themainresultisfollowing:Theorem　LetRbeoneofclassicaldomains,LbecharacteristicboundaryofR,f∈L2(L),H(z,ξ)beCauchykernelofRandF(z)=∫Lf(u)H(z,u)u　z∈R,(1)wheretherightisLebesgueintegral;uist…