# 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.