整环

Gauss整环上的二维AFT算法

Two-dimensional AFT Algorithm on Gauss Domain

设R为Dedekind整环，M是有限生成的扭R模，那么End（RM）为半完全环。

Let R be a Dedekind domain and M a finitely generated torsion R module , then End ( R ) is semi perfect .

卡内基·梅隆大学的计祘机科学系Gauss整环及其推广

Gauss Integral Ring and Its Extension Computer science Department , Shandong Teachers ' University

设R是一个整环，F是R[x]的商域，则R[x，x-1]是F的子环。

Let R is a domain , F is the quotient field of R [ x ] , then R [ x , x ~ - 1 ] is a subring of F.

结论：1、脑梗死患者Willis环整环完整者较少见。

Occurrence of the fully complete circle of Willis is low in patients with cerebral infarction . 2 .

把广义逆理论推广到模同态及模与环上，得到半单阿丁模的一个等价刻画以及一个整环R上的无挠模Q满足u。

Generalized inverse theories are applied on modules & rings and a equivalent condition of semisimple modules are given and we obtain a decomposition of torsionfree module Q over a domain R which satisfies w.

特别地，Dedekind整环R是PMM环当且仅当R的Picard群是幂可除的。

In particular , a Dedekind domain R is a PMM ring if and only if the Picard group of R is power divisible .

此外，描述了PTW整环的多项式环的相关性质；

Besides , we give the properties of the polynomial domains about PTW domains ;

证得非交换主理想整环R上右齐次线性方程组基础解系存在定理，给出R上右线性方程组解的表示。

This paper proves the existence theorem of the system of basic solutions for the right homogeneous linear equation sets over a non-commutative principal ideal domain R and gives the representation of the solutions for the right linear equation sets over R.

PTW整环的刻画

Characterizations of PTW Domains

另外，证明了R是赋值环当且仅当R是局部的Krull型整环，且R是TL整环，Spec（R）是全序。

Moreover , we prove that R is a valuation domain if and only if R is a quasi-local Krull type domain and R is a TL domain and Spec ( R ) is totally ordered .

关于KRULL型整环的性质的描述

Characterizations on Krull Type Domain

设n是特征为2的整环上由所有严格上三角（n+1）×（n+1）矩阵构成的李代数。本文的目的是确定李代数n的自同构群。

Let n be the nilpotent Lie algebra consisting of all strictly upper triangular ( n + 1 )×( n + 1 ) matrices over an integral domain R of characteristic 2.The aim of this paper is to give an explicit description of the automorphism group of the Lie algebra n.

证明了R是具有有限特征且满足局部主理想升链条件的pre-Krull整环当且仅当R是Krull整环。

We prove that R is a pre-Krull domain of finite character satisfying ascending chain conditions over principal ideals of the localization of R if and only if R is a Krull domain .

整环上的Kaplansky变换

The Kaplansky Transforms over Domains

设R是一个特征不是2的整环或是一个以2为单位的局部环，N是R上Dn（n≥4）型Chevalley代数的由正根基向量生成的幂零子代数。

Let R be a local communicative ring that contains 2 as a unit or a communicative integral domain of characteristic other than 2.Let N be the nilpotent subalgebra generated by positive root vectors of chevalley algebra of type D_n ( n ≥ 4 ) over R.

pre-Krull整环理论

The Theory of pre - Krull Domains

本文讨论了主理想整环的商环的乘法半群上的格林关系，确定了H-类的Sch櫣tzenberger群。

This paper investigates the multiplicative semigroup of a quotient ring of a principal ideal domain , characterizes Green 's relations and Sch ü tzenberger groups for H-classes .

近年来，如何把解决域上多条序列最短线性移性位寄存器综合问题的基本迭代算法（FIA）扩展到任意一个整环上，这一问题很受关注。

The fundamental iterative algorithm is usually used to synthesize minimum length linear feedback shift registers for generating prescribed multiple sequences . In recent years , how to extend it to an arbitrary integral domain has become a problem of great concern .

非交换主理想整环上的右线性方程组

System of Right Linear Equations over a Non-Commutative Principal Ideal Domain

一类整环中素元的条件及分解性质

Conditions of Prime Elements and Properties of Factorization of Some Integral Domains

交换整环上的上三角矩阵保对合的线性算子

Linear operators preserving involutions of upper triangular matrices over commutative integral domains

主理想整环的商环的乘法半群结构

The structure of multiplicative Semigroups of quotient rings for principal ideal comains

非交换主理想整环上分块矩阵的秩

The Rank of Partitioned Matrices over Non-commutative Principal Ideal Domain

交换主理想整环上交错矩阵的距离与极大集

Maximal Sets of Alternate Matrices over a Principal Ideal Domain

在整环上的几何空间中运动的分解

The Decomposition of Motion in Geometry Space of Integral Domain

主理想整环上的矩阵方程

The matrix equations over a principal ideal domain

给出了唯一分解整环上多项式不可约的一个判别法。

We give a method of determining irreducible polynomials over a unique factorization domain .

唯一分解整环上的局部结构

Local Structure Over Unique Factorization Domain

特征数≠2的非交换主理想整环上线性群的自同构

On the automorphism of linear groups over a non-commutative principal ideal domain of characteristic ≠ 2