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If $F$ is an integral domain, show that $F[x_1,\dots,x_n]$ is an integral domain.

Can anyone help out by giving me hints on how I should show that is an integral domain?

I would appreciate your help.

Sai82
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Lynnie
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1 Answers1

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Hint: show this for $F[x]$ first (one indeterminate), considering the polynomial degree; then use the fact that $F[x_1,\dots,x_{n-1},x_n]=R[x_n]$ where $R=F[x_1,\dots,x_{n-1}]$

egreg
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