An Analytic Zariski Structure Over a Field

Following the introduction and preliminary investigations of analytic Zariski structures in Peatfield and Zilber (Ann pure Appl Logic 132:125–180, 2005) an example of an analytic Zariski structure extending an algebraically closed field is provided. The example is constructed using Hrushovski’s method of free amalgamation, and a topology is introduced in which we can verify the analytic Zariski axioms.     

Asymptotic Sequences over a Module

Let (R, 𝔪) be a Noetherian local ring and M be a submodule of the free module F = R ^r with height(I _r (M)) > 0. Asymptotic sequences over M will be defined analogous to Rees’ definition of asymptotic sequences over an ideal. It is then shown that all maximal asymptotic sequences over M have the same length. This length gives a bound on the analytic spread of M. Namely, if s is the length of a maximal asymptotic sequence over M then l(M) ≤dim R + rank M ? 1 ? s. Equality holds if R is quasi-unmixed.     

On Prime Submodules of a Finitely Generated Free Module Over a Commutative Ring

In this article, we give a full characterization of prime submodules of a finitely generated free module F over a commutative ring R with identity. Also we study the existence of primary decomposition of a submodule of F and characterize the minimal primary decomposition of this submodule. We also describe the structure of prime submodules of a module over a Dedekind domain.     

The Analytic Spread of Monomial Ideals

Abstract

We compute the analytic spread of a monomial ideal I of the ring ?[[x ₁,…,x _n ]] in terms of the Newton polyhedron of I.     

The Annihilating-Ideal Graph of a Commutative Ring with Respect to an Ideal

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted 𝔸𝔾(R), is the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices joined by an edge when the product of the vertices is the zero ideal. We will generalize this notion for an ideal I of R by replacing nonzero ideals whose product is zero with ideals that are not contained in I and their product lies in I and call it the annihilating-ideal graph of R with respect to I, denoted 𝔸𝔾 _I (R). We discuss when 𝔸𝔾 _I (R) is bipartite. We also give some results on the subgraphs and the parameters of 𝔸𝔾 _I (R).     

一类解析多面体的奇异积分

本文利用Ｒ．Ｈａｒｖｅｙ和Ｊ．Ｐｏｒｋｉｎｇ的方法首先定义广义式的Ｃａｕｃｈｙ主值，利用同伦公式，借助积分变换技巧研究Ｗｅｉｌ型积分的边界性质，得到Ｐｌｅｍｅｌｊ公式．它有别于通常研究边界性质的方法．本文引入细复广义权和Ｃｈｏｑｕｅｔ型复广义权的概念，讨论了某些与复广义权相关的函数的拟连续性与细拟处处连续的关系．     

某个用Carlson-Shaffer算子定义的解析函数子类的性质(英文)

Let Hn（p）be the class of functions of the form f（z）=z p＋ ＋∞ Σ k=n akzk＋p,which are analytic in the open unit disk U={z：｜z｜1}.In the paper,we introduce a new subclass Bn（μ,a,c,α,p;φ）of Hn（p）and investigate its subordination relations,inclusion relations and distortion theorems.The results obtained include the related results of some authors as their special case.     

Some Results on Injective Modules Over a Ring of Krull Type

ABSTRACT

In this article, we study injective modules over a ring of Krull type A. Our main result is E(K/A)? ?_{ω∈Ω ^t} E(K/?_ω), where Ω ^t is a thin defining family of valuations of A. We also characterize the rings of Krull type A such that TE(K/A) is a cogenerator of the quotient category Mod(A)/?₀, where ?₀ is the thick subcategory of the modules with trivial maps into the codivisorial modules.     

Tensor and Torsion Products of Relative Injective Modules with Respect to a Semidualizing Module

Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In this paper, we show that C is generically dualizing if and only if the tensor products of injective and C-injective R-modules are injective. This leads to a characterization of dualizing modules as well as generalizes a result of Enochs and Jenda.     

Ideal Structure of Leavitt Path Algebras with Coefficients in a Unital Commutative Ring

For a (countable) graph E and a unital commutative ring R, we analyze the ideal structure of the Leavitt path algebra L _R (E) introduced by Mark Tomforde. We first modify the definition of basic ideals and then develop the ideal characterization of Mark Tomforde. We also give necessary and sufficient conditions for the primeness and the primitivity of L _R (E), and we then determine prime graded basic ideals and left (or right) primitive graded ideals of L _R (E). In particular, when E satisfies Condition (K) and R is a field, they imply that the set of prime ideals and the set of primitive ideals of L _R (E) coincide.     

On the Irreducible Components of the Form Ring and an Application to Intersection Cycles

Let A be a commutative Noetherian ring and I an ideal in A. We characterize algebraically when all the minimal primes of the associated graded ring G _I A contract to minimal primes of A/I. This, applied to intersection theory, means that there are no embedded distinguished varieties of intersection. The characterization is in terms of the analytic spread of certain localizations of I, the symbolic Rees algebra, and the normalization of the Rees algebra, and extends results of Huneke, Vasconcelos, and Martí-Farré.     

交换环上严格上三角矩阵半群的自同构(英文)

设R是任意含有单位元的交换环,N_n(R)是R上的所有n×n严格上三角矩阵组成的乘法半群.本文对N_n(R)的任意自同构给出了详细的描述.     

关于一类含有Dziok-Srivastava算子的多叶解析函数的包含关系和卷积性质

该文引进和研究了一类含有Dziok-Srivastava算子的新的多叶解析函数. 得到了这一函数类中的一些有趣的性质, 如包含关系, 卷积性质等. 这些结果改进和拓展了早期的一些工作. 同时也得到了其他一些新的结果.     

秩函数在研究独立空间拥有一对互斥基的特征上之作用

利用秩函数,本文给出如何判定一个独立空间拥有一对互斥基的一些充要条件.其目的是回答这样一个公开问题:在什么条件下,一个独立空间可以拥有一对互斥基.该问题是Welsh于1976年提出的.     

Cobalanced Extensions of a Torsion-Free Module by a Torsion Module Over an Integral Domain

Cobalanced extensions of torsion-free modules by torsion modules over domains are investigated. As in the case of Abelian Groups, these sequences will split if and only if the torsion-free module is a pure submodule of a vector module. Unlike this case, even the torsion-free modules of finite rank need not be locally completely decomposable. For 1-dimensional Noetherian domains, necessary and sufficient conditions are given for that to be true.     

Analytic Feynman Integrals of Functionals in a Banach Algebra Involving the First Variation

This paper deals with the analytic Feynman integral of functionals on a Wiener space. First the authors establish the existence of the analytic Feynman integrals of functionals in a Banach algebra S_α. The authors then obtain a formula for the first variation of integrals. Finally, various analytic Feynman integration formulas involving the first variation are established.     

由广义微分算子定义的某些解析函数类的优化性质

本文首先引入了由广义微分算子定义的某些$p$叶解析函数新子类$S_{p,q,\lambda}^{m,j,l}[A,B;\gamma]$ 和 $H_{p,q,\lambda}^{m,j,l}(\alpha,\beta)$, 然后研究了该子类的优化性质, 所得结果推广了某些已知结论.     

全矩阵环上理想包含图的自同构群

设R是一个环,其上的理想包含图,记为Γ_I(R),是一个有向图,它以R的非平凡左理想为顶点,从R的左理想I_1到I_2有一条有向边当且仅当I_1真包含于I_2.环R上的理想关系图,记为Γ_i(R),也是一个有向图,它以R为顶点集,从R中元素A到B有一条有向边当且仅当A生成的左理想真包含于B生成的左理想.设F_q为有限域,其上n阶全矩阵环记为M_n(F_q),本文刻画了环M_n(F_q)上的理想包含图以及理想关系图的任意自同构.