Definition:Decomposition


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


 * Abstract Algebra:
 * 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.
 * Another term for a factorization, usually used in the context of a polynomial ring.


 * Group Theory:
 * 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.