November 14th, 2007, 06:19 AM  #1 
Newbie Joined: Sep 2007 Posts: 10 Thanks: 0  field
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 onetoone. 
November 14th, 2007, 10:53 AM  #2 
Newbie Joined: Sep 2007 From: Nice, France Posts: 13 Thanks: 0 
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 onetoone. 

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