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

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]

2. Relevant equations

For a ring homomorphism,

f(a+b)= f(a) + f(b)

f(ab)= f(a)f(b)

3. 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.

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# Homework Help: Ring homomorphism and subrings

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