Definition:Total Ring of Fractions

Definition

Let $A$ be a commutative ring with unity.

The total ring of fractions of $A$ is the localization of $A$ at the set of its regular elements.

Also known as

The total ring of fractions of $A$ is also known as the total quotient ring of $A$. This should not be confused with quotient ring.

Also see

• Regular Elements of Ring form Multiplicative Subset

Special cases

• Definition:Field of Fractions

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.