Cancellation property

Summary

An element $a$ has the cancellation property for a binary operation when it can be removed from both sides of an equation $a \ast b = a \ast c$ or $b \ast a = c \ast a$. A structure in which every element is cancellable is called cancellative. Every group is cancellative by the cancellation laws, and the nonzero elements of an integral domain are cancellable for multiplication. Cancellative commutative semigroups are exactly those that embed in a group.