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.

$\blacksquare$