Proof of CRT ( for two modi) We must prove that f: Zm,m - Zm,x Zm given by is a bijedion. Proof O Fist check that f is well-delinad, i.e. that ļ is indeperdent of the choica of representadive x for the class Cx)m,m, O Show that f is one-to -ona O Show that ļ is onto This is trinial if f is one-to-one, as
Proof of CRT ( for two modi) We must prove that f: Zm,m - Zm,x Zm given by is a bijedion. Proof O Fist check that f is well-delinad, i.e. that ļ is indeperdent of the choica of representadive x for the class Cx)m,m, O Show that f is one-to -ona O Show that ļ is onto This is trinial if f is one-to-one, as
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 24E
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