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gotmilk04
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Homework Statement
Prove that if f:R-R' is a ring homomorphism, then
a) f(R) is a subring of R'
b) ker f= f[tex]^{-1}[/tex](0) is a subring of R
c) if R has 1 and f:R-R is a ring epimorphism, then f(1[tex]_{R}[/tex])=1[tex]_{R'}[/tex]
Homework Equations
For a ring homomorphism,
f(a+b)= f(a) + f(b)
f(ab)= f(a)f(b)
The Attempt at a Solution
In order to show something is a subring of something else, do I just show that the former satisfies the properties of a ring?
Like in a), would I show that f(R) is a ring?
I just need a little guidance please.