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 2021/6/16162021/6/16172021/6/16182021/6/16192021/6/16202021/6/16212021/6/16222021/6/16232021/6/16242021/6/16252021/6/16262021/6/16272021/6/16282021/6/16292021/6/1630三、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！