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Geekster
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Homework Statement
Suppose that f:R->Q (reals to rationals) is a ring homomorphism. Prove that f(x)=0 for every x in the reals.
Homework Equations
Homomorphisms map the zero element to the zero element.
f(0) = 0
Homomorphisms preserve additive inverses.
f(-a)=-f(a)
and finally,
f(a - b) = f(a) - f(b)
The Attempt at a Solution
My guess is go with contradiction and say, Suppose that f(a != 0) != 0 for some a in the reals.
But I don't see where to go from there. A hint or suggestion would be nice.