代数

From the history of Matrix and Transformation and the development of curriculum at home and abroad, putting matrix combined with the transformation, and orienting the study in 2×2 rank matrix, boosting matrix up the geometrical visualization as a algebra objects are a new perspective on knowing matrix.

从矩阵和变换的历史发展过程和国内外矩阵和变换的课程设置来看，把矩阵与变换相结合，并定位在2×2阶上研究矩阵，增强作为代数对象的矩阵的几何直观性，是认识矩阵的一个新视角。

The polynomial greatest common divisor is one of the most important polynomial contents, as which is not only the basic summary in the whole Higher Mathematics and Number Theory .

多项式最大公因式是多项式众多内容中十分重要的一项，它在整个高等代数、抽象代数、数论等科目当中，既是基础性的内容，也是很多其它项目研究中要求具有的储备知识。

This work gives an algorithm to simplify the rational curves in this situation. After the approximate proper index is defined, it is computed by solving the semi-algebra system. The greatest common divisor is obtained according to the computing process of approximate proper index.

为此，讨论了这类有误差的有理参数曲线，定义了近似非恰当参数形式和近似非恰当指数，并通过半代数系统计算近似非恰当指数；在给出近似非恰当指数的同时，得到近似最大公因子。

As an application, we also describe the Jordan automorphisms of the algebra of upper triangular matrices over commutative rings, and give a sufficient and necessary condition for a commutative ring being connected.

作为应用，我们还刻划了交换环上的上三角矩阵代数的Jordan自同构，并给出了一个交换环是连通环的充要条件。

We prove that the Jordan semi-triple derivable maps of the algebra of all n×n matrices over a 2-torsion free commutative ring with unity is the sum of an inner derivation and A_φ, where A_φis the image of A underφapplied entrywise andφis an additive derivation over R.

证明了作用在一个包含单位元的可交换的2-无挠环上的矩阵代数上的拟三重Jordan可导映射是一个内导子与A_φ的和(这里A_φ是A在φ下逐点作用的像)。

Polynomial function ; Finite commutative ring ; Finite commutative local ring; Teichmller representatives; Witt polynomial

基础科学，数学，代数、数论、组合理论多项式函数；有限交换环；有限交换局部环； Teichmller提升； Witt多项式

In the chapter two, we will recall some basic concepts and properties in commutative algebra and homological algebra.

在第二章中，作者介绍了交换代数和同调代数的一些基本概念和性质。

The central notion in commutative algebra is that of a prime ideal.

交换代数中最核心的概念就是素理想。

Commuta-tivity is one of important properties on rings. Study of commutativity is beneficial to discussion of other properties on rings.

同时，交换代数本质上是研究交换环的，这就使得环的交换性的研究变得很重要。

This thesis is mainly about to discuss the commutativity and the algebra properties of dual Toeplitz operators, and to prove the boundedness and compactness of products of Hankel operators in the several complex variables.

本文主要研究的是多变量的对偶Toeplitz算子的交换性和代数性质，以及Hankel算子乘积的有界性和紧性。

They go to town. Would you just ask them?

他们在城里你能问他们吗？

Ossein pretreated for a2 weeks period exhibited the maximum% yield incase of bone gelatin, while the yield from intact skin was higher than that realized incase of de-scaled skin.

预处理时间达2星期的骨胶原表现出最高的骨明胶百分产量，然而从未处理鱼皮中得到的产率比去鳞的鱼皮得到的要高。