Definition:Polynomial Ring/Embedding

Definition
Let $R$ be a commutative ring with unity. Let the ordered triple $(S, \iota, X)$ be a polynomial ring over $R$ in one indeterminate $X$.

The unital ring homomorphism $\iota$ is called the canonical embedding into the polynomial ring.

Multiple Indeterminates
Let $I$ be a set.

Let $(S, \iota, X)$ be a polynomial ring over $R$ in $I$ indeterminates.

The unital ring homomorphism $\iota$ is called the canonical embedding into the polynomial ring.

Also see

 * Canonical Homomorphism to Polynomial Ring is Ring Monomorphism