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March 14th, 2009, 06:35 PM  #1 
Newbie Joined: Mar 2009 Posts: 6 Thanks: 0  field, characteristic, surjective
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. 
March 14th, 2009, 09:15 PM  #2 
Member Joined: Aug 2008 Posts: 84 Thanks: 0  Re: field, characteristic, surjective
Remember that a function between two finite sets of the same cardinality is injective iff it is surjective. Injectivity, as you proved, is not difficult to come by, thus we get surjectivity for free! This is in fact a field automorphism.


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