ON DISTRIBUTIVE MODULES AND LOCALLY DISTRIBUTIVE RINGS

Distributive modules over artinian rings are characterized via module diagrams,andit is shown that a left artinian ring is(two-sided)locally distributive in case its leftindecomposable injective modules and projective modules are distributive.This latter resultis used to show that a locally distributive artinian ring and the endomorphism ring of itsminimal cogenerator have identical diagrams.     

The prüfer rings that are endomorphism rings of artinian modules

In this paper we characterize the (commutative) Priifer rings that can be realized as endomorphism rings of artinian modules over arbitrary associative rings with identity (Theorem 4.7). This characterization is obtained by determining the structure of ∑-pure-injective modules over Prufer rings (Theorems 3.4 and 3.5)     

Local Morphisms and Modules with a Semilocal Endomorphism Ring

We study local morphisms in the setting of general noncommutative rings. In particular, we apply local morphisms to study endomorphism rings of modules. We use our constructions to determine classes of modules with semilocal endomorphism rings. For instance, we prove that every finitely presented right module over a semilocal ring has a semilocal endomorphism ring.Alberto Facchini was partially supported by Gruppo Nazionale Strutture Algebriche e Geometriche e loro Applicazioni of Istituto Nazionale di Alta Matematica, Italy, and by Università di Padova (Progetto di Ateneo CDPA048343 “Decomposition and tilting theory in modules, derived and cluster categories”).Dolors Herbera was partially supported by the DGI and the European Regional Development Fund, jointly, through Project BFM2002-01390, and by the Comissionat per Universitats i Recerca of the Generalitat de Catalunya.     

半局部环的von Neumann正则性

主要借助small-内射模(环),给出半局部环的正则性和强正则性的一些等价刻画.     

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.     

正则模与半单Artin环

本文用则模的术语给出了半单Artin 环的刻划。得到如下三个条件的等价性:(1)R 是一个半单Artin 环;(2)每一个R-模都是正则模;(3)每一个单纯R-模都是正则模。     

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.     

Artin模上的替代结构

该文得到了Ａｒｔｉｎ模的一个替代结构，并进而证明了紧Ｈａｕｓｄｏｒｆｆ空间上连续函数环具有该替代结构．     

Characterizations of some rings with <Emphasis Type="Italic">C</Emphasis>-projective, <Emphasis Type="Italic">C</Emphasis>-(FP)-injective and <Emphasis Type="Italic">C</Emphasis>-flat modules

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations between C-flat modules and C-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.     

Projective modules are determined by their radical factors

We show that two infinitely generated projective modules are isomorphic whenever they have isomorphic factors modulo their Jacobson radical. Some applications of the result to semilocal rings with indecomposable non-finitely generated projective modules are given.