# Cancellative ring

From Commalg

## Definition for commutative rings

For commutative rings, the notion of cancellative ring coincides with the notion of integral domain.

## Definition for noncommutative rings

For noncommutative rings, there are three versions:

- Left-cancellative ring where the term on the left can be cancelled from any product
- Right-cancellative ring where the term on the right can be cancelled from any product
- Cancellative ring which is both left-cancellative and right-cancellative