单位元

Let G be a finite group, and S a subset of G not containing theidentity element 1. The Cayley digraph Cay on G with respect to S is definedas a directed graph with vertex set G and edge set {|g∈G, s∈S}. IfS~(-1)=S, then Cay is undirected and in this case, we view two directededges and as an undirected edge {u, v}. Obviously, the right regularrepresentation R of G, the acting group of G by right multiplication, is asubgroup of the full automorphism group AutCay(G, S of Cay.

给定有限群G，设S是G的不含单位元1的子集，群G关于子集S的Cayley有向图Cay是一个以G顶点集合，而以｛|g∈G，s∈S｝为边集合的有向图，特别地，若S~(-1)=S，则X=Cay是无向的，此时我们把一条无向边｛u，v｝等同于两条有向边和，易见，群G的右正则表示R，即G在G上的右乘作用，为图Cay的全自同构群AutCay

B 95 BIT 位元- The smallest amount of data. One binary digit.

资料的最小单位，一个二进位位数。

Once a particular identity skeleton has been decided on, it is possible to begin filling out the Cayley table.

一旦特定的单位元构架确定，就有可能开始填充出凯莱表。

Every maximal ideal of every commutative ring with identity is a prime ideal.

带有单位元的交换环的任何极大理想是素理想。

We introduce the concept of compatibility of an ordering of higher level with a valuation pair for a commutative ring with unit .

本文的主要目的是把域上高层序与赋值对的相容性推广到含单位元的交换环上来。

Let n ≥ 4 be a fixed integer, R be a unital commutative ring of characteristic not 2, and D_n be a D_n-type classical Lie algebra over R.

假设n是一个大于等于4的整数，R是特征非2的有单位元的交换环，D_n是环R上的D_n型李代数，N是D_n的一个极大幂零子代数。

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)。

Let R be a ring with identity. Then R is a division ring if and only if every unitary module over R is a free module.

R 是有单位元的环，它是除环的充分必要条件是其上的所有幺模都是自由模。

It follows that the identity element ''e'' is unique, and that all elements of ''Q'' have a unique

可以证明单位元''e''是唯一的，并且这时每一个''Q''中元素都有唯一的一个

In other words, F respects addition, multiplication and identity element .

换言之，F保持加，乘法和单位元。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。