《近世代数 环同态的性质》由会员分享，可在线阅读，更多相关《近世代数 环同态的性质（51页珍藏版）》请在金锄头文库上搜索。
1、In our classes,all the mobile phones should be switched off !2021/6/161上课啦！上课啦！The class is begin!2021/6/1622021/6/163第第 三三 章章 环与域环与域第第 19 讲讲 4 环的同态与同构环的同态与同构 2021/6/1642021/6/1652021/6/1662021/6/167他们同态吗？他们同态吗？2021/6/168一一 环环同同态态定定义义2021/6/1692021/6/16102021/6/1611 由上定义可知由上定义可知,一个环同态映射就是分别对一个环同态映射就
2、是分别对环的加法和乘法都满足环的加法和乘法都满足“保运算保运算”的性质的性质.利用这利用这一点一点,可以自然地得到可以自然地得到:二、环同态的性质二、环同态的性质2021/6/16122021/6/16132021/6/1614而而 同理同理, 2021/6/1615 所以所以 . . 则 2021/6/16162021/6/16172021/6/16182021/6/16192021/6/16202021/6/16212021/6/16222021/6/16232021/6/16242021/6/16252021/6/16262021/6/16272021/6/16282021/6/1629
3、2021/6/1630三、环同态基本定理三、环同态基本定理2021/6/16312021/6/16322021/6/16332021/6/16342021/6/16352021/6/16362021/6/1637四、环的扩张定理（挖补定理）四、环的扩张定理（挖补定理）2021/6/16382021/6/16392021/6/16402021/6/16412021/6/1642于是知于是知, 环环2021/6/16432021/6/16442021/6/16452021/6/16462021/6/16472021/6/16482021/6/16492021/6/1650 结束语结束语若有不当之处，请指正，谢谢！若有不当之处，请指正，谢谢！
