Definition:Polynomial Ring/Indeterminate

This page has been identified as a candidate for refactoring of basic complexity. Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code.

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).