Cancellative ring

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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