Suppose is a finite field of characteristic 3 and is the map defined by . Prove that is surjective. How do I do this? I know how to prove that it is an injective ring homomorphism. But I don't know how to prove it is surjective. Thanks.
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Originally Posted by sophia782 Suppose is a finite field of characteristic 3 and is the map defined by . Prove that is surjective. How do I do this? I know how to prove that it is an injective ring homomorphism. But I don't know how to prove it is surjective. Thanks. Since is finite and is injective it immeadiately means has to be surjective by the pigeonhole principle.
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