Polynomial Forms over Field form Integral Domain/Formulation 1/Proof 2
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Theorem
Let $\struct {F, +, \circ}$ be a field whose zero is $0_F$ and whose unity is $1_F$.
Let $X$ be transcendental in $F$.
Let $F \sqbrk X$ be the ring of polynomial forms in $X$ over $F$.
Then $F \sqbrk X$ is an integral domain.
Proof
We have from Ring of Polynomial Forms is Commutative Ring with Unity that $F \sqbrk X$ is a commutative ring with unity.
The result follows from Ring of Polynomial Forms is Integral Domain.
$\blacksquare$