Cancellative ring

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