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November 14th, 2007, 06:19 AM   #1
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Let F be a field of characteristic 2.
a) Prove that the function Φ:F →F given by Φ(x)=x^2 is a ring homomorphism.
b) Prove that it is also one-to-one.
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November 14th, 2007, 10:53 AM   #2
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a) 2=0, so (a+b)²=a²+b²+2ab=a²+b²
the others axioms are straithforward

b) untrue, it is only injective in general.
But, if F is finite, injective implies one-to-one.
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