(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all ring homomorphisms [tex]\phi[/tex]: Z [tex]\rightarrow[/tex] Z

[tex]\phi[/tex]: Z_{2}[tex]\rightarrow[/tex] Z_{6}

[tex]\phi[/tex]: Z_{6}[tex]\rightarrow[/tex] Z_{2}

2. Relevant equations

A function [tex]\phi[/tex]: R [tex]\rightarrow[/tex] S is called a ring homomorphism if for all a,b[tex]\in[/tex]R,

[tex]\phi[/tex](a+b) = [tex]\phi[/tex](a) + [tex]\phi[/tex](b)

[tex]\phi[/tex](ab) = [tex]\phi[/tex](a)[tex]\phi[/tex](b)

[tex]\phi[/tex](1_{R}) = 1_{S}

3. The attempt at a solution

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# Homework Help: Finding Ring Homomorphisms

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