弱半局部环的同调性质

环R称为弱半局部环,如果R/J(R)是Von Neumann正则环.给出了一个交换环是弱半局部环的充分且必要条件;还讨论了交换凝聚弱半局部环及其模的同调维数.     

半Artin环的同调维数

本主要研究半Artin环和完全环的等价性，以及半Artin环的同调维数．     

关于同调维数的一些注记

本文推广了环的R-序列的概念,引进了相伴R-序列,讨论了Jacobson根具有AR-性质的Noetherian环的同调维数及其结构性质,推广了交换局部环和半局部环的一些同调性质。     

Gr-凝聚环的小有限分次投射维数gr.fp.dimR

文 [1],[2 ]分别研究了Gr NoetherGr 局部 (半局部 )环的同调维数 ,本文主要进一步讨论Gr 凝聚Gr 半局部环的同调性质 .在§ 1中 ,主要刻画交换Gr 凝聚Gr 半局部环R的分次弱整体维数gr.gl.w .dimR ;在§ 2中 ,定义了分次环R的小有限分次投射维数gr.fp .dimR .刻画了gr.fp .dimR =gr .gl.w .dimR的Gr 凝聚环 .由于Gr Noether环是Gr 凝聚的 ,因而本文所得的结果对于Gr Noether环是自然成立的 .同时 ,本文所得的结果 ,也可视为文 [4 ]关于一般交换凝聚环相应结论的推广 .     

凝聚FP-环的结构

本文证明了有限弱整体维数的交换凝聚FP-环是GCD整环。特别地,有限整体维数的Noether FP-环是UFD。还研究了整体维数为2的FP-环。     

半局部环上二维线性群的构造

<正> B.R.McDonal 在[3]中把研究交换环上二维线性群的结构,特别当2为非单位时,作为以后典型群的一个研究方向而提了出来,并且他指出 N.H.T.Lacrox 的文章[2],局部环上的二维线性群,在当时是2非单位的交换环上二维线性群结构方面的唯一结果.而 N.H.T.Lacrox 在文章[2]中假定2为非单位.本文对剩余域元数个数均大于5的半局环上二维线性群,无论2为单位与否,统一讨论,解决了其结构问题.     

相对于余挠对的维数(英文)

本文介绍了右R-模的F-维数(C-维数)以及环R上整体F-维数(C-维数).利用同调方法,给出了平坦模维数的新刻画.另外,得到了von Neumann正则环和完全环的新刻画.     

群的Gorenstein同调维数

设$k$是一个弱维数有限的交换环, $G$是一个群. 本文讨论了群$G$具有有限的Gorenstein同调维数的标准.证明了群$G$的Gorenstein同调维数的有限性与群环$kG$的Gorenstein弱维数的有限性是一致的.进一步,我们给出了Serre定理的一个Gorenstein类比.推广了整环上$G$的Gorenstein同调维数的一些已知结果.     

广义半交换环的幂零结构

研究了广义半交换环的幂零结构,定义了一类新的环类,即幂零$\alpha$-半交换环.说明了$\alpha$-半交换环与半交换环, $\alpha$-半交换环和$\alpha$-刚性环等环密切相关,通过构造反例说明了幂零$\alpha$-半交换环未必是$\alpha$-半交换环.研究了幂零$\alpha$-半交换环的各种性质,推广和统一了与环的半交换性质有关的若干结论.     

F.P.—维数的合冲定理

1984年,Ho Kuen Ng在[1]中给出了交换环与模的有限表现维数(简称为F.P.—维数)的定义及若干有意义的重要结果.从此,有限表现性的讨论成为环论的热门课题之一.作者在[2]中将有限表现维数推广到非交换环上.并利用有限表现维数刻划了凝聚环,在[3]中讨论了有限表现维数的换环定理.在[4]中讨论了笛卡尔方形上的有限表现维数.丁南庆在[5]中推广了有限表现维数,给出了一种新维数——模的有限生成维数,在[6]中讨论了有限表现模的对偶     

Semiperfect Prüfer rings and FPF rings

The Asano-Michler theorem states that a 2-sided order R in a simple Artinian ringO is hereditary provided thatR satisfies the three requirements: (AM1) Noetherian; (AM2) nonzero ideals are invertible; (AM3) bounded. We generalize this in one direction by specializing to a semiperfect bounded orderR, and prove thatR is semihereditary assuming only that finitely generated nonzero ideals are invertible (=R is Prüfer). In this case,R ≈ a fulln ×n matrix ringD _n over a valuation domainD. More generally, we study a ringR, called right FPF, over which finitely generated faithful right modules generate the category mod-R of all rightR-modules. We completely determine all semiperfect Noetherian FPF rings: they are finite products of semiperfect Dedekind prime rings and Quasi-Frobenius rings. (For semiprime right FPF rings, we do not require the Noetherian or semiperfect hypothesis in order to obtain a decom-position into prime rings: the acc on direct summands suffices. The “theorem” with “semiperfect” delected is an open problem.     

Projective functors for quantized enveloping algebras

The object of this paper is to show that many of the known results concerning the structure of semiperfect FPF rings can be extended to a larger class of FPF rings. The main attributes of this larger class of rings are they have enough principle idempo-tents and idempotents lift modulo the Jacobson radical. We call these rings epi-semiperfect rings.     

Semiperfect ipri-rings and right Bézout rings

We present a survey of some results on ipri-rings and right Bézout rings. All these rings are generalizations of principal ideal rings. From the general point of view, decomposition theorems are proved for semiperfect ipri-rings and right Bézout rings.     

Elementary equivalence of incidence rings over semi-perfect rings

In this paper, we prove that if two incidence rings constructed by the same semiperfect ring and some two quasi-ordered sets are elementarily equivalent, then the given sets are elementarily equivalent.     

伪投射模的特征

本文运用伪投射模刻划了半单环、左遗传环、完全环、半完全环、拟完全环和半局部环的性质和特征。     

Strongly rational comodules and semiperfect Hopf algebras over QF rings

Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right C-comodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over a QF ring R is right semiperfect if and only if it is left semiperfect or — equivalently — the (left) integrals form a free R-module of rank 1.     

Uniquely Clean Elements in Rings

It is well known that every uniquely clean ring is strongly clean. In this article, we investigate the question of when this result holds element-wise. We first construct an example showing that uniquely clean elements need not be strongly clean. However, in case every corner ring is clean the uniquely clean elements are strongly clean. Further, we classify the set of uniquely clean elements for various classes of rings, including semiperfect rings, unit-regular rings, and endomorphism rings of continuous modules.     

On the integral cohomology of a sylow subgroup of the symmetric group

Projectivity classes, which dualize injectivity classes (cf.[ll]), are introduced and some examples are given. Characterizations of hereditary rings, semisimple rings, Noetherian rings, (semi-)perfect rings, quasi-perfect rings, semiregular rings, semiregular modules and F- semiperfect modules using projectivity classes are given. Finally, for a projectivity class P, P-projective covers are defined and similar results with “quasi-projective cover” substituted by “T-projective cover” will still hold. Our results unify and generalize several well known results by Golan, Huynh and Smith, Rangaswamy and Vanaja, Tiwary and Pandeya, and Xue.     

Idempotents and the multiplicative group of some totally bounded rings

In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2^ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.     

Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings

We say that is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) -module U, the dual module U* is a simple left (right) -module. We prove that a semiperfect ring is a DSM-ring if and only if it admits a Nakayama permutation. We introduce the notion of a monomial ideal of a semiperfect ring and study the structure of hereditary semiperfect rings with monomial ideals. We consider perfect rings with monomial socles.