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Number of elements in {xpn:x∈K}⊆K for a field K

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Charles Kyobe

User

( 5 months ago )

I have another question about ring theory.

Let KK b a field, with p>0p>0 its characteristic. Define the set T= {xK:xpn=x}T= {x∈K:xpn=x}. I had to prove that |T|pn|T|≤pn.


Research effort

We may assume that pp is prime, because otherwise the ring would have zero divisors. The exercise stated that TT itself is a field. I tried several things to prove the statement above. First of all xT  xpn=x  x(xp211)=0  x=0  or  x usr_profile.png

Vanshika Bhatt

User

( 5 months ago )

A polynomial of degree nn in a field FF has at most nn roots.

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