Question
If F is a field, show that U(F[x]) = F*.
Answer :
Word Count : 133
Let $F$ be a field. First observe that every nonzero constant polynomial $a\in F^\times$ is a unit in $F[x]$: its inverse is the constant polynomial $a^{-1}\in _____ _______ ___ _________ _________ ____ __________ ____ ______ _______.
_________ ______ _______ __________ ___ ______ ______ ____ _____ _______.
____ ___ ____ ___ ________ _____ ________ ________ _____ ___ _______.
____ ________ _________ ____ _______ _____ _________ ________ ______ _____ _____ ___.
___ ________ ____ _____ _________ _____.
_____ ______ _______ _________ _________ __________ ________ ___ __________ ___ _______ _____.
_________ _______ ____ ______ _________ __________ ______ __________ ___ _______ _________ ____.
___ _________ _____ _____ ___ __________ ___ ____ __________ _____.
______ ________ _______ ___ ___ _________ __________ ___ _________ ______ ________ _________.
__________ _____ ________ ________ _______ _____ ________ ________ ___ _____.
___ __________.
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Let $F$ be a field. First observe that every nonzero constant polynomial $a\in F^\times$ is a unit in $F[x]$: its inverse is the constant polynomial $a^{-1}\in _____ _______ ___ _________ _________ ____ __________ ____ ______ _______.
_________ ______ _______ __________ ___ ______ ______ ____ _____ _______.
____ ___ ____ ___ ________ _____ ________ ________ _____ ___ _______.
____ ________ _________ ____ _______ _____ _________ ________ ______ _____ _____ ___.
___ ________ ____ _____ _________ _____.
_____ ______ _______ _________ _________ __________ ________ ___ __________ ___ _______ _____.
_________ _______ ____ ______ _________ __________ ______ __________ ___ _______ _________ ____.
___ _________ _____ _____ ___ __________ ___ ____ __________ _____.
______ ________ _______ ___ ___ _________ __________ ___ _________ ______ ________ _________.
__________ _____ ________ ________ _______ _____ ________ ________ ___ _____.
___ __________.
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