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.     

关于拟圆性质的评注

设D是扩充复平面R-2中的单连通Jordan真子域,D*=R-2\D-是D的外部.本文肯定并证明 了K.Hag在1999年提出的如下两个悬而未决的问题:(1)D是Cigar域当且仅当D是OLC域; (2)D是Turning域当且仅当D*是Cigar域.     

w-Divisoriality in Polynomial Rings

We characterize all finite p-groups G of order p ⁿ (n ≤ 6), where p is a prime for n ≤ 5 and an odd prime for n = 6, such that the center of the inner automorphism group of G is equal to the group of central automorphisms of G.     

D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

Factorization in Integral Domains,IV

Let D be an integral domain such that every nonzero nonunit of D is a finite product of irreducible elements. In this article, we introduce and study several unifying concepts for the theory of nonunique factorization in D. They give a new way to measure, in some sense, how far an half-factorial domain (resp., bounded factorization domain, atomic domain) D is from being a UFD (resp., finite factorization domain, Cohen–Kaplansky domain) based on equivalence relations on the set of irreducible elements of D.     

超Cartan域上的积分表示

目的是研究第一类超Cartan域{(w,z) ||w|2 相似文献   

拟共形映射与John域

本证明了有界一致域必定是Hohn域和Jphn域的拟共不变性．     

Ascending Nets of Prüfer V-Multiplication Domains

Abstract

Let D be an integral domain, S ? D a multiplicative set such that aD _S  ∩ D is a principal ideal for each a ∈ D and let D ^(S) = ? _s∈S D[X/s]. It is known that if D is a Prüfer v-multiplication domain (resp., generalized GCD domain, GCD domain), then so is D ^(S) respectively. When D is a Noetherian domain, we obtain a similar result for the power series analog D ^((S)) = ? _s∈S D[[X/s]] of D ^(S). Our approach takes care simultaneously of both cases D ^(S) and D ^((S)).     

Some remarks and problems on complex homogeneous domains

We discuss some problems on rigidity of canonical realizations of complex homogeneous domains at ℂⁿ Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Some remarks and problems on complex homogeneous domains Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We discuss some problems on rigidity of canonical realizations of complex homogeneous domains at Cn     

Valuation and Pseudovaluation Subrings of an Integral Domain

Let R, S be two rings. We say that R is a valuation subring of S (R is a VD in S, for short) if R is a proper subring of S and whenever x ∈ S, we have x ∈ R or x ^?1 ∈ R. We denote by Nu(R) the set of all nonunit elements of a ring R. We say that R is a pseudovaluation subring of S (R is a PV in S, for short) if R is a proper subring of S and x ^?1 a ∈ R, for each x ∈ S?R, a ∈ Nu(R). This article deals with the study of valuation subrings and pseudovaluation subrings of a ring; interactions between the two notions are also given. Let R be a PV in S; the Krull dimension of the polynomial ring on n indetrminates over R is also computed.     

关于有界域的逆紧映照

本文对近20年来多复变函数的一个发展迅速的数学热门分支－逆紧映照作了一个回顾和整理。这是作者继续从事此方向研究的先声，也希望本文能为有志于此的研究者提供一些便利。本文从经典的结果开始，通过对逆紧映照在边界上的开拓及分支点的分布的讨论，详细地阐述了这些年来关于逆紧映照何时成为双全纯映照的若干结果。最后，对近年来关于逆紧映照另外的一些工作进行了简单的介绍。     

Commutative rings with two-absorbing factorization

We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local TAF-domains are the atomic pseudo-valuation domains.     

Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP.     

The Arc Distortion in QH Inner ψ-uniform （or Convex） Domains in Real Banach Spaces

Let D and D′ be domains in real Banach spaces of dimension at least 2. The main aim of this paper is to study certain arc distortion properties in the quasihyperbolic metric defined in real Banach spaces. In particular, when D′ is a QH inner ψ-uniform domain with ψ being a slow (or a convex domain), we investigate the following: For positive constants c,h,C,M, suppose a homeomorphism f: D → D′ takes each of the 10-neargeodesics in D to (c, h)-solid in D′. Then f is C-coarsely M-Lipschitz in the quasihyperbolic metric. These are generalizations of the corresponding result obtained recently by Väisälä.     

Unions of John domains

We study the question: When is the union of John domains a John domain?

     

On the Schwarz-Neumann method with an arbitrary number of domains

In this paper, a generalization of the Schwarz–Neumannmethod to more than two domains is given. We prove the convergenceand the numerical stability of the algorithm. The results applyto both bounded and unbounded domains, and are given for theweak solution of an elliptic problem with mixed boundary conditions.Numerical results are given for both bounded and unbounded domains.     

拟信息基,ω-代数Cpo,和SFP domain

G.Sam b in引入了(代数)信息基的概念,并证明了代数Scott D om a in范畴和信息基范畴是等价的.B.R.C.Bedrega l给出了ω-代数cpo和SFP dom a in的刻划.而G.Q.Zhang通过序结构给出了SFP dom a in的刻划.本文将引入了拟信息基的概念并给出了ω-代数cpo和SFP dom a in的刻划.