分次环与模范畴上的伴随函子

设 G是有限群 ,R是强 G-分次环 .本文证明了 R Re-与 Hom Re(R,- )都是从模范畴 R - mod到 Re- mod的“纯量”限制函子 F的伴随函子 ,并且两个函子 R Re-和Hom Re(R,- )是自然同构的 .     

PROJECTIVITY AND FLATNESS OF A MODULE OVER THE SUBRING OF INVARIANTS

Let k be a field and H a Hopf k-algebra with bijective antipode, R an H-module algebra over k and A = R#H the associated smash product. The fixed subring of R under H is denoted by S. Let P be an R#H-module. Thus P is an S-module. The aim of this paper is to study the projectivity of P as a module over S. We get a generalization of some results of J.J. Garcia and Angel Del Rio [4] Garcia, J. J. and Del Rio, A. 1995. On Flatness and Projectivity of a Ring as a Module Over a Fixed Subring. Mathem. Scandin., 76: 179–192.  [Google Scholar] of Ida Doraiswamy [8] Doraiswamy, I. 1982. Projectivity of Modules Over Rings with Suitable Group Action. Comm. Algebra, 10(8): 787–795. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] and of ours [[7] Guédénon, T. 1997. Algèbre Homologique Dans la Catégorie Mod_(R#U(g)). J. Algebra, 197(2): 584–614.  [Google Scholar], section 5].     

主理想整环上的线性方程组与矩阵方程

本文给出了含幺主理想整环Ｒ上线性方程组与矩阵方程解的判定与结构如下     

弱拓扑和强可容许拓扑之间的一个关系

本文对局部凸空间X及其对偶X′，建立了弱拓扑σ（X，X′）和强拓扑β（X，X′）之间的一个新关系，改进了有关（X，X′）－－可容许拓扑全体上的不变性结果。     

SELF-DUAL PERMUTATION CODES OVER FORMAL POWER SERIES RINGS AND FINITE PRINCIPAL IDEAL RINGS

In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.     

UNIQUE FACTORIZATION AND BIRTH OF ALMOST PRIMES

ABSTRACT

In studying unique factorization of domains we encountered a property of ideals. Using that we define the notion of almost prime ideals and prove that in Noetherian domains almost prime ideals are primary. We also prove that in a regular domain almost primes are precisely primes. Further, we define strictly nonprime ideals and study some inter relations between almost prime ideals, strictly nonprime ideals and factorization of ideals.     

IDEAL STRUCTURE OF UNIFORM ROE ALGEBRAS OVER SIMPLE CORES

This paper characterizes ideal structure of the uniform Roe algebra B*(X) over simple cores X. A necessary and sufficient condition for a principal ideal of B*(X) to be spatial is given and an example of non-spatial ideal of B*(X) is constructed. By establishing an one-one correspondence between the ideals of B* (X) and the ω-filters on X, the maximal ideals of B*(X) are completely described by the corona of the Stone-Cech compactification of X.     

Tube中的模同态与模分解

本文讨论管（tube)范畴中的模同态,在不可分解模上运用[4]中特殊生成元的定义,进一步研究了管范畴中模同态的一些性质,得到了关于同态g:L→Mh,l的导出模L的直和分解及其核的构造。     

正则乘子Hopf代数上Yetter-Drinfel'd模范畴中的自同构代数

本文研究了正则乘子Hopf代数上Yetter-Drinfel''d模范畴中自同构代数的问题.利用乘子Hopf代数以及同调代数理论中的方法,获得了Yetter-Drinfel''d模范畴中两个自同构代数是同构的结果,推广了Panaite等人在Hopf代数中的结果.     

主理想整环上保对合矩阵的线性映射

设R是特征不为2的交换主理想整环,Mn（R）表示R上n阶全矩阵模,本文基底生成元的方法刻划Mn（R）上保对合矩阵的R-线性映射的形式。     

表大偶數為一個不超過三個素數的乘積及一個不超過四個素數的乘積之和

<正> V.Brun最初在1920年證明了:每一充分大的偶數可表為兩個各不超過9個素數的乘積之和.簡記之為(9,9).後來,不少數學家改進與簡化了Brun方法,因此,Brun的結果也得到相應的改進,     

交换主理想整环上立方幂等矩阵的线性保持

设Ｒ（≠Ｆ_３）是特征不为２的交换主理想整环,Ｍ_ｎ（Ｒ）定义Ｒ上的ｎ×ｎ矩阵模,本文刻划当ｎ≥ｍ时从Ｍ_ｎ（Ｒ）到Ｍ_ｎ（Ｒ）的保持立方幂等矩阵的线性映射的形式,由此推广了Ｃｈａｎ和Ｌｉｍ的一个结果（［１,定理３］）．     

乘法模的性质及判定

本文给出了关于乘法模的一个判定定理的两个极端条件下乘法模的构造，同时给出一个例子说明无限生成乘法模的存在性。     

THE GOLDBACH-VINOGRDOV THEOREM WITH THREE PRIMES IN A THIN SUBSET

1.IntroductionandStatementofResultsIn1937,Vinogradovi7]provedthatJ(N),thenumberofrepresefltationsofanilltegerNassumsofthreeprimes,satisfiesthefollowingasymptoticformulawherea(N)isthesingularseries,andu(N)>>1foroddN.Itthereforefollowsthateverysufficientlylargeoddintegeristhesumofthreeprimes.ThissettledtheternaryGoldbachproblem,andtheresultisreferredtoastheGoldbach-Vinogradovtheorein.ManyauthorshaveconsideredthecorrespondingproblemswithrestrictedconditionsposedonthethreeprimesintheGoldbach…     

STABLE AND UNSTABLE IDEAL PLANE FLOWS

IntroductionWe COnsider SOllltlollS     

关于剩余类环Zn和Galois环GR（p^e，n）上的理想双同态门限体制

本文讨论了两类特殊环上的理想双同志门限体制．利用门限体制的完善性及同态性，证明了以剩余类环Zn，和Galois环GR(p^e，n)为密钥空间的理想双同志(t，ι)-门限体制是平凡的．