n. 1. (in an additive algebraic structure) a law asserting that whenever a + b = a + c then b = c follows. In a group this is an immediate consequence of the existence of inverse elements. 2. (in an multiplicative algebraic structure) a law asserting that whenever a×b = a×c and a ≠ 0 then b = c follows. A commutative ring is an integral domain exactly when the cancellation law holds for the ring multiplication.