分次余同调维数

主要把Ａｕｓｌａｎｄｅｒ－Ｂｕｃｈｓｂａｕｍ定理推广到分次环情形，更为精细地刻划了交换ＮｏｅｔｈｅｒＧｒ－局部正则Ｚ－分次环的同调维数．

伪内射模与特殊环

研究了伪内射模的性质,用伪内射模刻画了半单环,Noether、V-环,半Artin环和半局部环,得到的主要结果为:(1)伪内射模的完全不变子模是伪内射模;(2)R是半单环当且仅当伪内射模与半单模一致当且仅当半本原模是伪内射模,且本质基座的模是伪内射模当且仅当基座为0的模是伪内射模,伪内射模的直和伪内射;(3)R半Artin环当且仅当基座为0的模伪内射;(4)R是半局部环当且仅当R为左良好环且半本原模是伪内射模.

自内射环族的矩阵环

主要证明以下结论 :( 1 )若 {αβα|α,β∈ B}是右忠实的双模同态族 ,则 R是局部左自内射环当且仅当 {Rα}α∈ A是左自内射环族且对任意α,β∈ A,μαβ∶ Rαβ→ Hom Rβ( Rβα,Rβ)是同构当且仅当对 A的任意非空有限子集 B,作为左 e BRe B-模 ,有 e BRe B e BE( R) e B;( 2 )若 {αβα|α,β∈ A}是右忠实的双模同态族 ,{ββγ|β,γ∈A}是左忠实的双模同态族 ,则 R是局部左 PF环当且仅当每一个 Rα都是左 PF环 ,α∈ A;( 3 )若 {αβα,αββ|α,β∈ A}是双模同构族 ,则 ( i) R是局部左 Artin环 (局部左 Noether环 )当且仅当 Rα是左 Artin环 (左 Noether环 ) ,α∈ A;( ii) R是局部 QF环当且仅当 {Rα}α∈ A是 QF环族且对任意α,β∈ A,μαβ∶ Rαβ→ Hom Rβ( Rβα,Rβ)

Maximal codes

In this work we try to introduce the concept of Maximal codes that are built over rings, more precisely we will give Maximal codes for special rings, Namely that the notion of maximal codes has been used by Chritophe Chapote, these maximal codes are constructed over finite fields, and these codes are used for coding and decoding.

I-投射模及其性质

设(R,m)是交换的Noether局部环,I是R中的理想,M是有限生成的R-模.给出了I-投射模的定义及M是I-投射模的等价条件,讨论了I-投射维数、整体I-投射维数等相关性质.

分式分次环、分式分次模与分次局部化方法

局部化（Localization）方法是交换代数中一个重要工具，通过研究一个代数簇（AlgebraicVariety）在某点或某点附近的局部性质，往往可以把握代数簇的整体特性。局部化方法已成为整个代数学中一个有效的一般方法。本文引进分式分次环（Gradedringoffractions）、分式分次模（Gradedfractionalmodule）以及分次局部化（Gradedlocalization）方法的概念，并对它们进行了系统的研究。所得结论推广和改进了文献[1]中的若干结果。

局部化与Gorenstein投射和Gorenstein内射模

设R是一个交换诺特环且S是R的乘法闭子集.如果G是一个有限生成的(半)Gorenstein投射右R-模,则S^(-1)G是一个有限生成的(半)Gorenstein投射右S^(-1)R-模.如果S^(-1)R是忠实平坦的,则R满足Gorenstein投射猜想可推出S^(-1)R满足Gorenstein投射猪想.特别地、In如果R是交换阿廷环且E一个有限生成的Gorenstein内射右R-模,则S^(-1)E是一个有限生成的Gorenstein内射S^(-1)R-模.

半局部环上模的内射维数及其它

研究Noether半局部环上模的内射维数,推广了局部环的相应结论,从而丰富了半局部环的理论.

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.

Envelopes of Commutative Rings

Given a significative class F of commutative rings, we study the precise conditions under which a commutative ring R has an S-envelope. A full answer is obtained when F is the class of fields, semisimple commutative rings or integral domains. When .F is the class of Noetherian rings, we give a full answer when the Krull dimension of R is zero and when the envelope is required to be epimorphic. The general problem is reduced to identifying the class of non-Noetherian rings having a monomorphic Noetherian envelope, which we conjecture is the empty class.

Characterization of Weak I Sequences

In [5], Zhou defined the notion of weak I sequences and characterized such se-quences by Koszul cohomology and local cohomology methods. The aim of this paper is to characterize weak I sequences by means of Ext functor.

TOWARD A THEORY OF WEAK I SEQUENCES

The author introduces a notion of weakIsequences and characterizes such sequences by means of homological methods.This notion extends the notion of weakMsequences and thus extends the notions of generalized Cohen Macaulay modules and Buchsbaum modules to more general cases.

On Standard Ideals

In the paper, we study a class of standard ideals which are more general than the m-primary standard ideals discussed in [2]. We will prove an important equality concerning I-weak sequences; thus a generalization of the equality of [2] is established.