关于半群环与群环的链条件的等价性

给出了将半群环的链条件转化为群环的链条件的一个定理,并由此将［１］中的结果推广到半群环的情形．     

半群环的右Artin性

本文研究了一般半群环的右Artin性的刻划问题，改进了JanOkniski在[3]中的结果，并给出了半群环是右Artin环的刻划．最后进一步指出在一定条件下，R[S1]和R[S1]的链条件是等价的．     

模右逆半群

半群的格方法－通过研究半群的子半群格来研究半群的特征和结构，与幂等元方法是研究半群的两种有效方法，本文利用这两种方法，完全确定了具有模的全右逆子半群的右逆半群的结构。     

半群半直积的主投影性质(英文)

本文研究了半群半直积的主投影性质.利用适当半群,获得了右主投影半群半直积的充分和必要条件,推广了半直积的一些结果.     

关于Clifford半群S和Brandt半群S的S↑^的构造

设Ｓ是半群,Ｓ↑＾是Ｓ↑＾上所有一一偏的右平移构成的逆半群。在本文中证明了,对Ｃｌｉｆｆｏｒｄ半群Ｓ＝［Ｙ;Ｇα,φα,β］,Ｓ↑＾≌ｌｉｍ｛Ｇα｝α∈Ｙ,而对Ｂｒａｎｄｔ半群Ｓ＝Ｂ（Ｇ,Ｉ）,Ｓ↑＾≌ＧｗｒＪ（Ｉ）。     

交换半群环的分式环

设含幺交换环Ｒ对其乘法子集Ｔ的分式环为ＲＴ，交换幺半群Ｓ在其子半群∑处局部化为Ｓ∑本文证明了Ｒ［Ｓ］对于Ａ的分环式环Ｒ［Ｓ］ＡＭ 构于半群环ＲＴ［Ｓ∑］。     

Noether环理想的性质

Noether交换环是一类非常重要的环,本文主要对Noether交换环进行了研究和讨论,得到了Noether交换环、Noether整环的若干性质;并推广了文[1]中的部分结果.     

Artin环与Noether环的一个刻画

在[1]文中利用极大左理想刻画了Noether环,本文引进Noether左理想、Artin左理想、m左理想等概念(当I是环R的极大左理想时, I既是Noether、Artin的也是m的,此时m=1。),证明了[1]文中相应的结论,给出了相应的Artin环的刻画。 定义1 环R的左理想I称为Artin(Noether),如果R/I是Artin(Noether)R模。 定义2 环R的左理想I称为m理想,如果R/I的任何R子模都可由m个元生成。 本文的主要结论:     

On the Finiteness of Noetherian Rings with Finitely Many Regular Elements

Let R be a left Noetherian ring and ZD(R) be the set of all zero-divisors of R. In this paper, it is shown that if R \ ZD(R) is finite, then R is finite.     

Projective ideals of skew polynomial rings over HNP rings

Let R be an hereditary Noetherian prime ring (or, HNP-ring, for short), and let S?=?R[x;σ] be a skew polynomial ring over R with σ being an automorphism on R. The aim of the paper is to describe completely the structure of right projective ideals of R[x;σ] where R is an HNP-ring and to obtain that any right projective ideal of S is of the form X𝔟[x;σ], where X is an invertible ideal of S and 𝔟 is a σ-invariant eventually idempotent ideal of R.     

Semidistributive and distributively decomposable rings

A module is said to be distributive if the lattice of all its submodules is distributive. A module is called semidistributive if it is a direct sum of distributive modules. Right semidistributive rings, as well as distributively decomposable rings, are investigated. Translated fromMatematicheskie Zemetki, Vol. 65, No. 2, pp. 307–313, February, 1999.     

Injective dimension of Weyl algebras over affine coefficient rings

The concern of this paper is to derive formulas for the injective dimension of then- th Weyl algebraA _n (R) in casek is a field of characteristic zero andR is a commutative affinek-algebra of finite injective dimension. For the casen=1 we prove a more general result from which the above result follows. Such formulas can be viewed as generalizations of the corresponding results given by J. C. McConnell in the caseR has finite global dimension.Project supported in part by the National Natural Science Foundation for Youth     

有限扩张环

证明了环的有限扩张性可以传递到矩阵环上;通过PP环,半遗传环以及有限余非奇异环刻划了有限扩张环,并推广了文献[2]的定理2.1; 对于FGF与CF猜测,给出了部分肯定的回答,即右有限扩张右CF环是右CEP的,从而是右aritian的,改进了文献[6]的定理3.7.     

Weight filtrations via commuting automorphisms

We consider a filtration of theK-theory space for a regular Noetherian ring proposed by Goodwillie and Lichtenbaum and show that its successive quotients are geometric realizations of explicit simplicial Abelian groups. The filtration in weightt involvest-tuples of commuting automorphisms of projectiveR-modules. It remains to show that the Adams operations act appropriately on the filtration.Supported by NSF grant DMS 90-02715. I thank Tom Goodwillie, Stephen Lichtenbaum, Friedhelm Waldhausen, Steven Landsburg, and Stephen Ullom for useful discussions and ideas.     

Uniserial Noetherian centrally essential rings

Abstract

It is proved that a ring R is a right uniserial, right Noetherian centrally essential ring if and only if R is a commutative discrete valuation domain or a left and right Artinian, left and right uniserial ring. It is also proved that there exist non-commutative uniserial Artinian centrally essential rings.     

Injective modules and linear growth of primary decompositions

The purposes of this paper are to generalize, and to provide a short proof of, I. Swanson's Theorem that each proper ideal in a commutative Noetherian ring has linear growth of primary decompositions, that is, there exists a positive integer such that, for every positive integer , there exists a minimal primary decomposition with for all . The generalization involves a finitely generated -module and several ideals; the short proof is based on the theory of injective -modules.

     

弱Ⅰ序列的刻画

在文献[5]中,周才军定义了弱Ⅰ序列,并利用Koszul上同调和局部上同调的方法刻画了这种序列.本文利用Ext函子刻画了弱Ⅰ序列.