Thread: Frobenius map

I need help on this problem





Thanks

Originally Posted by capitalX

I need help on this problem

Let R be a commutative ring of prime characteristic p. Show that the Frobenius map x->x^p is a ring homomorphism from R to R.

Thanks

i expect someone who's studying algebra knows this much from elementary number theory that for any prime

number and integer we have: so: hence, since R is commutative,

for any besides it's obvious that

therefore the map is a ring homomorphism. Q.E.D.