# Definition:Free Module on Set

Jump to navigation
Jump to search

It has been suggested that this page or section be merged into Definition:Free Module.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 `{{Mergeto}}` from the code. |

## Definition

Let $R$ be a ring.

This article, or a section of it, needs explaining.In particular: For this concept to be more easily understood, it is suggested that the ring be defined using its full specification, that is, complete with operators, $\struct {R, +, \circ}$ and so on, and similarly that a symbol be used to make the module scalar product equally explicit.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it.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 `{{Explain}}` from the code. |

Let $I$ be an indexing set.

The **free $R$-module on $I$** is the direct sum of $R$ as a module over itself:

- $\ds R^{\paren I} := \bigoplus_{i \mathop \in I} R$

of the family $I \to \set R$ to the singleton $\set R$.

## Also see

### Special case

## Sources

There are no source works cited for this page.Source citations are highly desirable, and mandatory for all definition pages.Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |