Krull–Schmidt Failure - Pure Mathematics - Algebra Dictionary Definition A situation in an additive category where an object admits two decompositions as a finite direct sum of indecomposable objects that are not pairwise isomorphic, violating the uniqueness clause of the Krull–Schmidt theorem.
Krull–Schmidt Failure - Pure Mathematics - Algebra Dictionary Definition A situation in an additive category where an object admits two decompositions as a finite direct sum of indecomposable objects that are not pairwise isomorphic, violating the uniqueness clause of the Krull–Schmidt theorem.