Failure of Cancellation - Pure Mathematics - Algebra Dictionary Definition The phenomenon in an additive category (e.g., modules) where A ⊕ C ≅ B ⊕ C does not imply A ≅ B; that is, direct-sum cancellation fails and isomorphism after adding the same summand does not force isomorphism of the original summands.
Failure of Cancellation - Pure Mathematics - Algebra Dictionary Definition The phenomenon in an additive category (e.g., modules) where A ⊕ C ≅ B ⊕ C does not imply A ≅ B; that is, direct-sum cancellation fails and isomorphism after adding the same summand does not force isomorphism of the original summands.