I是环R的理想,在I的加法陪集\bar{R}=R/I上定义+和\times运算:(a+I)+(b+I)=a+b+I,,(a+I)(b+I)=ab+I,那么\bar{R}也是环,叫做商环(quotient ring)。存在 canonical/natural surjective ring homomorphism\pi:R\rightarrow R/I, \pi(a)= a+I,ker\ \pi=I。
一个双射的环同态称为环同构(ring isomorphism)。在这种情况下,我们写为 R \cong S 若存在一个环同构 \phi:R\rightarrow S - 一个环同态 \phi:R\rightarrow S 是,特别的,一个阿贝尔群的群同态 \phi:(R,+)\rightarrow (S,+) 。因此,在群论上,我们有 \phi(0_R)=0_S 和\phi(-r)=-\phi(...
quotient ringQ 开头单词回到顶部短语词组短語 短语词组 短語 quotient near ring 商擬環 right quotient ring 右分式環 maximal quotient ring 極大商環 left quotient ring 左商環 maximal right quotient ring 極大右商環 symmetric quotient ring 對稱商環 left right quotient ring 左商環 Gaussian quotient ring...
The concepts of fuzzy semiideal and fuzzy quotient ring is introduced and some properties of fuzzy semiideal are discussed. 引入模糊半理想與模糊商環的概唸,討論了模糊半理想的一系列性質,竝建立了關於模糊半理想的對應定理。 Recently, Ningbo First Hospital for the three students from Africa, presented ...
ring n. [C] 1.圈;环;环形物 2.戒指;耳环 3.年轮;围成一圈的人(或物) 4.圆形灶盘 5.马戏场;拳击场 6.(不法)集团,帮派 v. [T] 1.包围;围住(+with) latern(ring) 润滑环 ring...up 给...打电话 ring oil 油环润滑 sale ring n. 围拢在拍卖者周围的购买人 scarf ring n. 领带...
商环(Quotient Ring):交换代数中通过理想生成的环结构 这些应用均体现quotient作为'关系约简结果'的深层数学意义。 三、术语对比与辨析 与quotient相关的四则运算术语构成完整体系:加法(sum)、减法(difference)、乘法(product)、除法(quotient)。特别要注意在微积分中,quotient rule(商法则...
Theidealsin a quotient ring are in aone-to-one correspondencewith ideals in which contain the ideal . In particular, the zero ideal in corresponds to in . In the example above from the integers, the ideal of even integers contains the ideal of the multiples of 6. In the quotient ring, ...
美 英 un.商环 网络商换 英汉 网络释义 un. 1. 商环 释义: 全部,商环,商换
Chapter 10 defines a quotient ring, or factor ring, as the set of cosets of a ring modulo an ideal. All the ideals in a euclidean ring are shown to be principal ideals. As in groups, the Morphism Theorem for rings connects the kernel and image of a ring morphism. It is shown how ...
Browse Nearby Words quotient group quotient ring quotlibet See all Nearby Words Cite this Entry Style “Quotient ring.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/quotient%20ring. Accessed 31 Mar. 2025. Copy Citation ...