Definition:Decomposition


 * Decomposition (Topology): A set of subsets of a subset $S$ of $\R^n$ such that there exist isometries on such subsets which form a partition of $S$.


 * Decomposition (Abstract Algebra): A set of closed algebraic substructures of an algebraic structure $S$ (usually a group or a ring) whose intersection is the identity and whose internal direct product is isomorphic with $S$ itself.


 * Group Decomposition: A set of subgroups of a group $G$ whose intersection is the identity and whose internal group direct product is isomorphic with $G$ itself.