整环

Then R is an Archimedean domain if and only if a is contained in some minimal prime ideal of R for every nonzero nonunit a.

则有R是阿基米德整环当且仅当a含在R的某个极小素理想中。

Letbe Ra PID. M_n the n×n full matrix algebra over R,and f denotethe linear bijection over M_n.

设R是主理想整环，M_n是尺上全矩阵代数，f为M_n上的可逆线性算子。

The last part of the chapter is devoted to the elementary factorization theory of commutative monoids with cancellation property and of commutative domains

后一部分主要介绍了关于交换幺半群的关于消去律的初等的因式分解理论以及交换整环的理论

In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.

本文在介绍了K〓理论和相对K〓理论以及与K〓理论有关的2阶典型群的基本概念及主要成果之后，对于虚二次域代数整环的K〓群的计算，非GE〓泛的虚二次域的子环以及K〓到K〓的自然同态的余核的生成元集等问题进行了研究。

By using the Euclidean algorithm , the matrix solution of indefinite equation of first degree is discussed.

利用高斯整环上的欧几里德算法给出求解高斯整环上的多元一次不定方程通解的矩阵解法，同时利用MATLAB数学软件给出相应的计算机求解高斯整环上一次不定方程的通用程

The structure of R with small homological dimension is discussed.

至于整体维数有限的左右Noether局部环是否是整环，至今尚未解决。

II, Polynomial rings on a general field( on contrast of those over a number field): concepts of ring, ideals, field and several special rings as domains, principal ideal domains and unique factorization domains, the unique factorization theory of polynomial rings.

二、一般域上的多项式理论（是数域上多项式理论的推广）：学习环、域和几类特殊结构的环（整环、主理想环，唯一分解环等）的概念，多项式环的唯一分解定理；三、线性代数：讲述一般数域上的向量空间理论（是数域上向量空间理论的继续和推广），模的概念，主理想环上的模的结构及其线性变换的若当标准型等；四、一元多项式的解及域论：学习域扩张及其相关概念，伽罗瓦理论，用伽罗瓦定理判断根式解的存在性。

In this paper, we introduce the concepts of the great common P-divisor, least common P-multiple of two distinct nonzero elements x, y in arbitrary unique factorization domain R, and denote them byp, and p respectively.

在本文中，作为通常的整数环Z上的最大公因子和最小公倍数的推广，我们在惟一分解整环R上定义了最大公P-因子和最小公P-倍元，分别记为_P和_P。

The technique of this paper is to reduce the problems in the case of rings to that of fields by taking specializations of orderings and the quotient fields of domains .

本文的方法是通过取序的特殊化以及整环的商域，使环的情形下的问题转化到域的情形来解决。

The congruences on orthorings are studied. Results concerning congruences and congruence-pairs on orthorings are obtained.

对纯整环并半环上的同余进行了研究，得到了纯整环并半环上关于同余和同余对的一些结果。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。