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

 * Definition:Field of Fractions