内射模的t－平坦性

设Ｒ为环，ｔ是左Ｒ－模范畴的一个遗传挠理论．文中证明了下述各点等价：（１）每个内射左Ｒ－模是ｔ－平坦的；（２）每个ｔ－有限表现左Ｒ－模的内射包络是ｔ－平坦的；（３）每个ｔ－有限表现左Ｒ－模是自由Ｒ－模的子模；（４）每个ｔ－有限表现左Ｒ－模是自反的且其对偶模是Ｈ－有限生成的．     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

F－V－环的广义内射性刻划

设Ｆ是含单位元的结合环Ｒ上的左Ｇａｂｒｉｅｌ拓朴，称Ｒ是Ｆ－Ｖ－环，如果商范畴（Ｒ，Ｆ）－Ｍｏｄ中的所有单对象都是内射对象。本文我们利用左Ｒ－模的ｖＮ－内射性及拟内射性给出Ｆ－Ｖ－环的特征刻划。     

T拟内射模与TQI环

本文定义并刻划了Ｔ拟内射模与Ｔ拟内射包，证明了ＷＧ－ｃｏｃｒｉｔｉｃａｌＴ拟内射模的自同态环为正则非奇异右自内射环．最后讨论了Ｔ拟内射模与Ｔ内射模一致的环，即ＴＱＩ环．还给出了Ｇａｂｒｉｅｌ拓扑Ｇ中每个右理想Ｔ拟内射的几个等价条件     

正则环与YJ—内射性

献「１」中,Ｍｉｎｇ．Ｒ．Ｙ．Ｃ引进了ＹＪ－内射模的概念,且指出正则环上的每个模均是ＹＪ－内射模,那么反之如何呢？「１」中做了一些结果,本拟就这个问题作进一步讨论。     

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．     

广义FP—内射模、广义平坦模与某些环

左（右）R－模A称为GFP－内射模，如果ExtR(M,A)=0对任－2－表现R－模M成立；左（右）R－模称为G－平坦的，如果Tor1^R(M,A)=0(Tor1^R(AM)=0)对于任一2－表现右（左）R－模M成立；环R称左（右）R－半遗传环，如果投射左（右）R－模的有限表现子模是投射的，环R称为左（右）G－正而环，如果自由左（右）R－模的有限表现子模为其直和项，研究了GFP－内射模和G－平坦模的一些性质，给出了它们的一些等价刻划，并利用它们刻划了凝聚环，G－半遗传环和G－正则环。     

关于左A—内射环

本文主要证明了：（1）适合右零化子升链条件的左A－内射环为QF环。（2）适合左零化子升链条件的左f-内射环为QF环。（3）若对环R的任意左理想A，B和右理想I满足r(A∩B）=r(A) r(B),rι(I)=I，则R为半完全环且有本质左基座，特别地，右CF的左A－内射环（或E(RR)为投射左R－模）为QF环。     

关于分次本质右理想

设 Ｒ是 Ｇ－分次,本文讨论了环 Ｒ的相关环 Ｒ,Ｒ＃ Ｇ^*, Ｒｅ, Ｑ（Ｒ）, Ｒ^G, Ｒ*Ｇ及 Ｒ的正规化扩张Ｓ的非奇异性,右一致性,右基座之间的关系．当Ｒ_Ｒ是ＹＪ－内射模时,证明了Ｊ（Ｒ）＝Ｚ（Ｒ）。     

有限生成平坦模的投射性和内射性

本文给出了每个有限生成平坦模内射，既投射又内射的环类的刻划．给出了每个有限生成平坦模既投射又内射这一环类的分类     

The connes spectrums of certain finite non-abelian groups

In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated.     

$f$-投射与$f$-内射模

Let R be a ring. A fight R-module M is called f-projective if Ext^1 （M, N） = 0 for any f-injective right R-module N. We prove that （F-proj,F-inj） is a complete cotorsion theory, where （F-proj （F-inj） denotes the class of all f-projective （f-injective） right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules.     

Characterizations of Strongly Regular Rings

ＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｓｏｆＳｔｒｏｎｇｌｙＲｅｇｕｌａｒＲｉｎｇｓＺｈａｎｇＪｕｌｅ（章聚乐）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈｕ２４１０００）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...     

Note on residually finite rings

This paper is on the subject of residually finite (= RF) modules and rings introduced by Varadarajan [93] and [98/99]. Specifically there are several theorems that simplify proofs and generalize some results of Varadarajan, namely.

Theorem 1. An RF right R-module is finitely bedded (= has finite essential socle iff M is finite.

Corollay. If T is a right RF woth just finitely many simple ringht R-modules, them R is fimite.

Theorem 2. A commutative ring R is residually finite iff every local ring R_m at a maximal ideal m is finite.     

On the structure of indecomposable injective modules 1

For a ring R, the following two conditions are equivalent:.

(1) If E is an indecomposable injective right R-module, then End E_R is a field (not necesarily commutative).

(2) Every co-irreducible rigtht ideal is critical.

Since (2) has been characterized ideal-theoretically, this amounts to an ideal-theoretical characterization of (1). These rings come up to the study of (QI) rings in which every quasi-injective module is injective.     

关于基本可数生成子模的扩张性

称左R-模M是ecg-扩张模,如果M的任意基本可数生成子模是M的直和因子的基本子模.在研究了ecg-扩张模的基本性质的基础上,本文证明了对于非奇异环R,所有左R-模是ecg-扩张模当且仅当所有左R-模是扩张模.同时我们还用ecg-拟连续模刻画了Noether环和Artin半单环.     

Zip模(英文)

A ring R is called right zip provided that if the annihilator τR（X） of a subset X of R is zero, then τR（Y） = 0 for some finite subset Y C X. Such rings have been studied in literature. For a right R-module M, we introduce the notion of a zip module, which is a generalization of the right zip ring. A number of properties of this sort of modules are established, and the equivalent conditions of the right zip ring R are given. Moreover, the zip properties of matrices and polynomials over a module M are studied.     

关于强正则环的刻画

通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的:①R是强正则环;②R是半素的左GP-V′-环,且每一个极大的左理想是广义弱理想;③R是半素的左GP-V′-环,且每一个极大的右理想是广义弱理想.     

On nonsingular right fpf rings

A right FPF ring is one over which every finitely generated faithful right module is a generator. The main purpose of the article is to givp the following cnaracterization of certain right FPF rings. TheoremLet R be semiprime and right semihereditary. Then R is right FPF iff (1) the right maximal ring of quotients Q_r (R) = Q coincides with the left and right classical rings of quotients and is self-injective regular of bounded index, (ii) R and Q have the same central idem-potents, (iii) if I is an ideal of R generated by a ma­ximal ideal of the boolean algebra of central idempotent s5 R/I is such that each non-zero finitely generated right ideal is a generator (hence prime), and (iv) R is such that every essential right ideal contains an ideal which is essential as a right ideal

In case that R is semiprime and module finite over its centre C, then the above can be used to show that R is FPF (both sides) if and only if it is a semi-hereditary maximal C-order in a self-injective regular ring (of finite index)

In order to prove the above it is shown that for any semiprime right FPF ring R, Q _lcl (R) exists and coincides with Q_r(R) (Faith and Page have shown that the latter is self-injective regular of bounded index). It R is semiprime right FPF and satisfies a polynamical identity then the factor rings as in (iii) above are right FPF and R is the ring of sections of a sheaf of prime right FPF rings

The Proofs use many results of C. Faith and S Page as well as some of the techniques of Pierce sheaves