Definition:Polynomial Ring/Indeterminate

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Definition

Let $R$ be a commutative ring with unity.

Single indeterminate

Let $\left({S, \iota, X}\right)$ be a polynomial ring over $R$.


The indeterminate of $\left({S, \iota, X}\right)$ is the term $X$.

Multiple Indeterminates

Let $I$ be a set.

Let $\left({S, \iota, f}\right)$ be a polynomial ring over $R$ in $I$ indeterminates.


The indeterminates of $\left({S, \iota, f}\right)$ are the elements of the image of the family $f$.


Also known as

The indeterminate(s) of a polynomial ring are sometimes seen referred to as variable(s).