An isomorphism of graphs Gand H is a one to one correspondance of the vertex sets of Gand H. Such that any two vertices u and v of G are adjacent in H if and only if f(u) = f(u)² + f(v)² O f(u) and f(v) are adjacent in H O flu) and f(v) are contained in G but not contained in H O f(u * v) = f(u) + f(v)

An isomorphism of graphs Gand H is a one to one correspondance of the vertex sets of Gand H. Such that any two vertices u and v of G are adjacent in H if and only if f(u) = f(u)² + f(v)² O f(u) and f(v) are adjacent in H O flu) and f(v) are contained in G but not contained in H O f(u * v) = f(u) + f(v)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 21E: Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by...

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Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by (a0+a1x++anxn)=[ a0 ]+[ a1 ]x++[ an ]xn, where [ ai ] denotes the congruence class of Zk that contains ai. Prove that is an epimorphism from Z[ x ] to Zk[ x ].