- #1
phyguy321
- 45
- 0
Homework Statement
Find all ring homomorphisms [tex]\phi[/tex]: Z [tex]\rightarrow[/tex] Z
[tex]\phi[/tex]: Z2 [tex]\rightarrow[/tex] Z6
[tex]\phi[/tex]: Z6 [tex]\rightarrow[/tex] Z2
Homework 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](1R) = 1S