扩张环上的$\Sigma$-相伴素理想

作为对相伴素理想与幂零相伴素理想的推广,我们在本文中引进了$\Sigma$-相伴素理想的定义,探讨了$\Sigma$-相伴素理想的基本性质,证明了Ore扩张环$R[x;\alpha,\delta]$、斜洛朗多项式环$R[x,x^{-1};\alpha]$及斜幂级数环$R[[x;\alpha]]$的$\Sigma$-相伴素理想都分别可以用环$R$的$\Sigma$-相伴素理想来刻画,从而将相伴素理想与幂零相伴素理想的一些已有结论推广到更一般的情形.     

除环上的全阵环的极小右理想与半素F-环

说环R是F-环,如R含一有限非零元集X,使对任意α∈R,若αR≠0,则αR∩X≠φ(傅昶林)。半素F-环可表为有限个除环上的全阵环的直和(周毅强)。有人指出,这个命题的逆命题是不对的,今给出环为半素F-环的充要条件,先看除环上的全阵环。 设D为一除环,n>1为一自然数,R为D上n阶全阵环。极小右理想均为主右理想、取α=(α_(ij))≠0∈R,设其中某α_(ij)≠0∈D,则     

McCoy环的Ore扩张(英文)

本文研究了斜多项式环与微分多项式环的McCoy性质,证明了如果环R是α-compatible和可逆的,那么斜多项式R[x;α]是McCoy环当且仅当环R是McCoy环;同时我们也证明了如果环R是δ-compatible与可逆的,那么微分多项式环R[x;δ]是McCoy环当且仅当环R是McCoy环.因此本文对McCoy环的相关结论进行了推广.     

诣零半交换环上的Ore扩张

本文研究诣零半交换环上的Ore扩张环的性质.利用对多项式的逐项分析方法,我们证明了:设α是环R上的一个自同态,δ是环R上的一个α-导子.如果R是(α,δ)-斜Armendariz的(α,δ)-compatible环,则R[x;α,δ]是诣零半交换环当且仅当环R是诣零半交换环;如果R是诣零半交换的(α,δ)-compatible环,则R[x;α,δ]是斜Armendariz环.所得结果推广了近期关于斜多项式环的相关结论.     

关于循环环的理想、素理想和极大理想

研究了循环环R=的理想、素理想和极大理想的个数和结构,得到了如下结论:1)理想:(1)若|R|=∞,则R共有无穷多个理想:;(2)若|R|=n,设n的正因数个数为T(n),则R共有T(n)个理想:.2)素理想:(1)若|R|=∞,设a^2=ka(k≥0),①当k=0时,R的素理想只有R;②当k>0时,R的素理想共有无穷多个,它们是:{0}、R及;(2)若|R|=n>1,设a^2=ka,0≤k.3)极大理想:(1)若|R|=∞,则R有无限多个极大理想,它们是;(2)若|R|=n>1,设n的互不相同的素因数个数为ψ(n),则R共有ψ(n)个极大理想:(pa|p是n的素因数).     

含有极小单侧理想单纯环的结构

一个矩阵称为几乎零矩阵,如果矩阵的元素除了有限多个外皆为零。一个矩阵环称为几乎零矩阵环,若它的每个元素都是几乎零矩阵。本文我们获得了如下的主要结果,任何含有极小单侧理想的单纯环必可以模同构地嵌入到一个除环上的几乎零矩阵环中。     

关于含有极小单侧理想的本原环结构

本文用双侧模方法代替通常有限拓扑方法来描述具有极小单侧理想本原环结构,结果包含深化和扩展了本原环的熟知基本定理——结构定理及同构定理(参见文献[1])。     

微分算子环的素理想

大家知道,多复变典型域调和函数论的基本事实是:设R为四类典型域之一,Γ为其特征边界,△是R的Laplace-Beltrami算子,f∈C~∞(R)称为调和的,如果△f=0。设f为调和函数,其在Γ的连续边界值为ψ,那么f在R中的值由以下Poisson积分给     

微分算子环的素理想

本文利用代数的方法与基本结果，对钟家庆关于微分算子理想的结构基于Ｈ．Ｍａａｓｓ的调和齐式分解所得到的结果，在复系数情形给出了一个纯代数的简短证明，在证明中不需要关于微分算子的齐次性假设     

亚BCI-代数的$(\alpha,\beta)$-软理想

首先将软集的参数集赋予亚BCI-代数, 给出了亚BCI-代数的$(\alpha,\beta)$-软理想的概念.当$U=[0,1], \alpha=U, \beta=\phi$时,相应地就得到了亚BCI-代数的犹豫模糊理想的概念.研究了亚BCI-代数的$(\alpha,\beta)$-软理想的一些重要性质.最后讨论了亚BCI-代数的$(\alpha,\beta)$-软理想的同态像和原像的性质.     

理想上的广义$(\theta,\phi)$-导子的正交性

In this paper,necessary and sufficient conditions concerning the orthogonality and the composition of a couple of generalized （θ,φ）-derivations on a nonzero ideal of a semiprime ring are presented.These results are generalizations of several results of Breˇsar and Vukman,which are related to a theorem of Posner on the product of two derivations on a prime ring.     

Ore Extensions of Ore Domains

Let R be a right Ore domain and φ a derivation or an automorphism of R. We determine the right Martindale quotient ring of the Ore extension R[t; φ] (Theorem 1.1). As an attempt to generalize both the Weyl algebra and the quantum plane, we apply this to rings R such that k[x] ? R ? k(x), where k is a field and x is a commuting variable. The Martindale Quotient quotient ring of R[t; φ] and its automorphisms are computed. In this way, we obtain a family of non-isomorphic infinite dimensional simple domains with all their automorphisms explicitly described.     

强正则 $(\alpha,\beta)$-族和平移强正则 $(\alpha,\beta)$-几何

本文给出了强正则$(\alpha,\beta)-$族的概念,它是[4]和[5]中$SPG-$族概念的推广.进一步,给出了一种用强正则 $(\alpha,\beta)-$族构造强正则$(\alpha,\beta)-$几何的方法.另外,本文还证明了由强正则$(\alpha,\beta)-$线汇构造的强正则$(\alpha,\beta)-$几何是平移强正则$(\alpha,\beta)-$几何;当$t-r>\beta$时,反之亦成立.     

关于超代数$(\alpha,\beta,\gamma)$-超导子的一个注记

This paper is concerned with two results for （α, β, γ）-superderivations of general superalgebras over the field of complex numbers.     

Fibers in Ore Extensions

Let R be a finitely generated commutative algebra over an algebraically closed field k and let A=R[t;,] be the Ore extension with respect to an automorphism and a -derivation . We view A as the coordinate ring of an affine noncommutative space X. The inclusion RA gives an affine map : XSpecR, and X is a noncommutative analogue of A ¹×SpecR. We define the fiber X _p of over a closed point pSpecR as a certain full subcategory ModX _p of ModA. The category ModX _p has the following structure. If p has infinite -orbit, then ModX _p is equivalent to the category of graded modules over the polynomial ring k[x] with degx=1. If p is not fixed by , but has finite -orbit, say of size n, then ModX _p is equivalent to the representations of the quiver à _n–1 with the arrows all going in the same direction. If p is fixed by , then ModX _p is equivalent to either Modk or Modk[x]. It is also shown that X is the disjoint union of the fibers X _p in a certain sense.     

具有对称自同态的环及其扩张

Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetricα-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α(1) = 1, then R is a symmetric α-ring if and only if R[x]/(x n) is a symmetric ˉα-ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q(R) the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q(R) is a symmetric ˉα-ring. Among others we also show that if a ring R is weakly 2-primal and(α, δ)-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric ˉα-ring.     

关于空间$S(\Omega,\Sigma,\mu)$与$L^\beta(\Omega,\Sigma,\mu)$上的次加上半连续$\alpha$-正齐性泛函

本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了S（Ω，∑，μ）与L^β（Ω，∑，μ）分别不存在非零的上半连续、次加、α-正齐性泛函（分别有0≤α≤1和β〈α≤1）的充要条件．     

具有可反测地线的$(\alpha,\beta)$-度量

本文我们得到了$(\alpha,\beta)$-度量的测地系数$G^{i}(x,y)$和其逆$G^{i}(x,-y)$有相同Douglas曲率的充分必要条件.这个充分必要条件恰好是$(\alpha,\beta)$-度量具有可反测地线的充分必要条件.