关于局部Noether模

本文证明了如下结果：左 Ｒ－模 Ｍ是局部 Ｎｏｅｔｈｅｒ模当且仅当σ［Ｍ］中的任意Ｍ－内射左Ｒ－模的直和是一个有限余生成左Ｒ－模和一个拟连续（或连续,直内射）左Ｒ－模的直和．     

R-拟连续模的不可分分解

设R是环,M是R-拟连续左R-模.如果R关于形如l（m）,m∈M的左理想满足升链条件,则M可写成一致子模的直和.     

关于G-Matlis自反模的换环定理

设Ｒ和Ｔ是Ｎｏｅｔｈｅｒ完备半局部环，Ｒ→Ｔ是环同态．本文证明了，若Ｔ是有限生成或ＡｒｔｉｎＲ－模，Ｍ为Ｇ－Ｍａｔｌｉｓ自反Ｒ－模，则对所有ｎ≥０，Ｅｘｔ^Ｒ_ｎ（Ｔ，Ｍ），Ｅｘｔ^Ｒ_ｎ（Ｍ，Ｔ），Ｔｏｒ^Ｒ_ｎ（Ｔ，Ｍ）以及Ｔｏｒ^Ｒ_ｎ（Ｍ，Ｔ）均是Ｇ－Ｍａｔｌｉｓ自反Ｔ－模．所得结果推广了Ｒ．Ｂｅｌｓｈｏｆ的结果．     

关于T-S模的直觉模糊群的直积特征

首先将T模、S模的概念推广,并研究了推广的T-S模的基本性质,进而分别定义了在对偶模意义下直觉模糊群的外直积与内直积.最后,证明了直觉模糊群的两种直积在一定条件下是同构的.     

Banach空间上的左可逆算子的稳定性

主要讨论了Banach空间上左可逆算子在线性运算上的稳定性及一些摄动问题,并通过反例证明了对于Banach空间上的左可逆算子A和B,R（A）∩R（B）＝{0}不是λA＋B（λ∈C）为左可逆算子的必要条件。     

Characterization of V-modules by Relative Quasi-continuity

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＲｂｅａｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙａｎｄＭａｌｅｆｔＲ ｍｏｄｕｌｅ .ＡｌｅｆｔＲ ｍｏｄｕｌｅＵｉｓｃａｌｌｅｄＭ ｉｎｊｅｃｔｉｖｅｉｆ,ｆｏｒｅｖｅｒｙｓｕｂｍｏｄｕｌｅＮｏｆＭａｎｄｅｖｅｒｙｈｏｍｏｍｏｒｐｈｉｓｍ :Ｎ→Ｕ ,ｃａｎｂｅｅｘｔｅｎｄｅｄｔｏａｈｏｍｏｍｏｒｐｈｉｓｍ ψ :Ｍ→Ｕ .ＡｌｅｆｔＲ ｍｏｄｕｌｅＭｉｓｃａｌｌｅｄａＶ ｍｏｄｕｌｅｂｙＲａｍａｍｕｒｔｈｉ[1]ａｎｄＴｏｍｉｎａｇａ[2 ](ａｎｄｉｓｃａｌｌｅｄａｃｏ ｓｅｍｉｓ…     

A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

For locally compact groups G, Kuan Yuan studied a notion of inner amenability groups, that is, if there exists an inner invariant mean on G. In this article, among other things, the author investigates the inner amenability on a locally compact group G. The author gives sufficient conditions and some necessary conditions about G to have an inner invariant mean.     

核局部凸空间的一个新特征

Ａ．Ｐｉｅｔｓｃｈ＾［１］在讨论核局部凸空间时给出了两类矢值序列空间ｌ１［Ｘ］和ｌ１｛Ｘ｝。本文建立了矢值序列空间ｌ１［Ｘ］及ｌ１｛Ｘ｝和连续线性算子空间Ｌ（ｃ０，Ｘ）及绝对可和算子空间ＡＳ（ｃ０，Ｘ）之间的拓扑同胚关系。通过ｃ０上的矢值算子类Ｌ（ｃ０，Ｘ）和ＡＳ（ｃ０，Ｘ）及其上的拓扑等价关系，对局部凸空间Ｘ是核空间给出了一个新的特征刻划。     

EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES

Let R be a commutative Noetherian ring and p be a prime ideal of R such that the ideal pRp is principal and ht(p)≠ 0. In this note, the anthors describe the explicit structure of the injective envelope of the R-module R/p.     

关于完全环与Noether环

（ｉ）环Ｒ是左完全环，当且仅当存在一个基数ｃ，使得任意平坦左Ｒ－模是一个拟投射模和一个ｃ－限制的ＥＳ－模的直和。（ｉｉ）Ｒ是左Ｎｏｅｔｈｅｒ环，当且仅当存在一个基数ｃ，使得任意内射左Ｒ－模的直和是一个（拟）连续模和一个ｃ－限制的ＥＳ－模的直和。     

Banach空间上一类由算子导出的局部凸拓扑

本文我们研究了由半范簇｛ＰＴ｜Ｔ∈ψ（Ｅ，Ｅ１）｝在Ｅ上导出的局部凸拓扑σＥ（Ｅ１），其中ＰＴ（ｘ）＝Ｔｘ的范数，ｘ∈Ｅ。首先我们给出了拓扑σＥ（Ｅ１）＝ω和σＥ（Ｅ１）＝Ｅ上的范数的等价条件，接着讨论了在σＥ（Ｅ１）下的紧性与完备性，最后利用空间稠密特征和关于无穷基数幂等的Ｈｅｓｓｅｎｂｅｒｇ定理进一步研究了σＥ（Ｅ１）与Ｅ上的范数的关系，证明了当Ｅ的稠密特征足够大时在ω和Ｅ上的范数间有无穷多个     

EXTENSlONS OF HARDY MODULES OVER THE POLYDISK ALGEBRA

1.IntroductionAHilbertmoduleisaHilbertspaceHwhichisalsoamoduleoverafunctionalgebraA,i.e.,thereisanassociativebilinearmultiplicationAxHHwhichiscontinuousinbothvariables.ThefirstsystematicstudyofHilbertmodulesappearedinthemonographofDouglasandPoulsen[...     

ON THE FINITENESS PROPERTIES OF THE GENERALIZED LOCAL COHOMOLOGY MODULES

Abstract

The question, posed in Crawley and Jónsson (Crawley, P., Jónsson, B. (1964). Refinements for infinite direct decompositions of algebraic systems. Pacific J. Math. 14:797–855), whether the finite exchange property implies the unrestricted exchange property for any modules, is still open. In this note we obtain the equivalence of the finite exchange property and the unrestricted exchange property for the class of modules whose endomorphism rings are Abelian.     

EXTENSIONS OF HARDY MODULES OVER THE POLYDISK ALGEBRA

In this paper, the Ext groups of Hardy modules over the polydisk algebra A(D^n) are calculated, Of particular importance is that the calculating of Ext-groups is closely related to harmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidity of Hardy submodules over A(D^n) for n > 1.