查询词典 commutative

The number of polynomial function over a finite commutative ring. This paper is on the basis of the research for the first question.With the structure of finite commutative ring,we know that a finite commutative ring can be expressed by direct sum of some finite commutative local rings.

本文主要基于对问题一的研究，并由有限交换环的构造可以知道，有限交换环可以由一些有限交换局部环的直和表示，于是就将问题简化到对有限交换局部环上多项式的判定。

Besides having a some insight into theinternal structure of operator algebras,it gives a greatimpetus to the development of modern mathematics towords thenon-commutative direction,especially to the developement ofnon-commutative geometry,non-commutative algebraical topologyas well as non-commutative algebraical geometry.

除了反映算子代数自身的内在性质之外，它还对于现代数学朝着非交换的方向发展起着积极的推动作用，特别对于&非交换微分几何&，&非交换的代数拓朴&，甚至&非交换的代数几何&等非交换的数学学科的发展具有重要的影响。

If R satisfies =0 for any elements x ,y in R then ⑴when k =1, R is commutative;⑵when R has the unity, R is commutative;⑶when R has at least one right regular element and f 2 (t 1,t2) has no terms with degree1 such that Fn= F then R iscommutative when R has at least one right regular element. Here we would like to point out that the above results generalized the results of Fu changlin ,moreover generalized some results of other references . This results enriched the commutative conditions of any ring.

若任取R 中元x， y均有=0 那么⑴k =1时R 为交换环；⑵R 有单位元时R 为交换环；⑶f_2 (t_1，t_2)中t_2的次数不小于k -1且R 中至少有一个右正则元时R 为交换环。

In chapter 3, the concepts of M-matrix and H-matrix over a commutative Banach algebra have been proposed, and some of their important properties and applications in linear systems over a commutative Banach algebra have been studied. For usual complex matrix, the Bellman inequality with Hadamard product has been proved.

第三章，提出了交换Banach代数上M一矩阵及H一矩阵的概念，研究了其一些重要性质，并给出了在交换Banach代数上线性系统中的应用；对有限维复矩阵，证明了关于 Hadamard乘积的 Bell.an不等式。

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, we introduce the notion of M-valuation systems for a commutative ring, and investigate the M-valuations from the inside of a commutative ring.

在本文中，我们引进了M-赋值系统的概念，从环的内部给出交换环上M-赋值的结构。

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。

In chapter three, we study the strongly cleaness of some 3 times3 matrix rings over a commutative local ring and prove that if R is a commutative local ring, Then TM_{3} is a strongly clean ring.

本文第三章主要研究可换局部环上的某些三角矩阵环的强clean 性，并且证明如果 R是可换局部环，则 TM_{3}是强clean矩阵环。

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

"A set of elements having two operations, designated addition and multiplication , satisfying the conditions that multiplication is distributive over addition and that both operations are associative and commutative for all elements of the set, with the exception of the additive identity element, which is not commutative in respect to multiplication ."

"一组元素，进行加法和乘法两种运算，满足条件：乘法运算需分配于加法之中，这组元素要将这两种运算结合且换进行，附加的就乘法而言不可交换的恒等元素除外。"

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。