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I have to find all the units in the ring $F[x]$ where $F$ is a field.

Clearly all polynomials of degree 0 are units as they are in the field F.

Now suppose $\alpha(x)\beta(x)=1$ which gives $\mbox{deg}(\alpha(x))=-\mbox{deg}(\beta(x))$ which gives $\mbox{deg}(\beta(x)=\mbox{deg}(\alpha(x)=0$ so the units are precisely the polynomials of degree.

Is this correct?

Thanks for any help

Clearly all polynomials of degree 0 are units as they are in the field F.

Now suppose $\alpha(x)\beta(x)=1$ which gives $\mbox{deg}(\alpha(x))=-\mbox{deg}(\beta(x))$ which gives $\mbox{deg}(\beta(x)=\mbox{deg}(\alpha(x)=0$ so the units are precisely the polynomials of degree.

Is this correct?

Thanks for any help

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