查询词典 commutative

Mathematics 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.

域，体：进行加法和乘法两种运算的一组数，满足如下条件，即乘法分配律同样适用于加法分配律，各数在做加法和乘法两种运算中可相互结合并交换，但在乘法中不可交换的加性恒等幺元除外

In this paper, we discuss effect algebra and related topics. The main results are the following:1. Effect algebra is a commutative algebraic structure. To get a non-commutative algebraic structure.we introduced the concepts of left difference and right difference, and we also introduced the concept of the Bi-difference sets, the concept of pseudo-difference poset, and proved that pseudo-difference poset is equivalent to pseudo-effect algebra.

效应代数描述的是具有交换性的量子系统，我们借助于差运算的思想研究了不可交换的量子逻辑结构，建立了左差、右差、伪差偏序集、双差集等概念，证明了伪差偏序集与伪效应代数等价，并得到了双差集的幺半群表示定理。

By using properties of scalar matrices over semirings,we generalize algebraic properties for the automorphisms of matrix algebras over commutative rings and obtain some algebraic properties for the automorphisms of matrix algebras over commutative semirings.

在这一章中，我们首先利用半环上常量矩阵的性质把环上矩阵代数的性质拓广到半环上，获得了交换半环上矩阵代数自同构的一些代数性质，接下来采用积和式的方法证明任意非负交换半环上n阶矩阵代数Tn的自同构的n次幂必为内自同构。

The relation between the rank of a matrix and the rank of its compound adjoint matrix over any commutative ring is given.

建立交换环上矩阵A的秩与A的复合伴随矩阵C*k的秩之间的关系。

M porous structure confirms transmission of body fluid of human body and ingrowths of mineral and fiber tissue, then made it firmer combine with around tissue of human body and the commutative pores was favourable for affusion of bioactive HA.

本实验采用东北大学陶瓷研究所研制成功的由Ti粉和Ni粉为主要原料，采用TiH_2和NH_4HCO_3作为造孔剂，通过粉末冶金方法制备的多孔NiTi合金，并采用真空灌注羟基磷灰石的方法取得的种植体的新材料，在添加TiH_2做为造孔剂的基础上在Ti：Ni原子比为50%：50%的试样中添加NH_4HCO_3做为第二种造孔剂后，试样中的气孔经检测是由100～500μm的大孔、1～50μm小孔和1μm以下的微孔组成，产生了合理的粗化表面并同时得到了固位良好的生物涂层。

Since there are special courses devoted to commutative algebra and algebraic geometry, these parts are not included in the present course.

因此选择的内容应有普适性、示范性、基础性、重要性和可教性。过于专门化的理论或细节不是这门课的任务。

Computing integral closure of a finite extension is not only an important problem in commutative algebra, but also in algebraic geometry and algebraic number theory.

计算有限扩张的整闭包不但是交换代数中的一个核心问题，也很受代数几何以及代数数论发展的推动。

Finally, We prove that every generalized a associative BCI algebra determine a commutative pomonoid .

最后我们证明了每个广义a－结合BCI－代数可确定一个交换偏序幺半群。

We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

The combination rule of the method satisfies commutative law and associative law, fully uses information of conflict evidences, and solves three kinds of problems appeared in conflict evidences combination process.

该组合方法满足结合律和交换律，充分利用冲突证据信息，解决了冲突证据组合中的三类问题。

Who? I never heard of him, Paul said, before asking teammate James Posey if he had heard of him.

赛后，科比说，他一直都是一名非常出色的射手，今天他打得很棒。

When I joined the company, I rotated around the different sections.

我加入这个公司时，轮换过几个不同的部门。