# Definition:Decomposition

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Decomposition** may refer to:

- 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.

- Number Theory:
- Prime Decomposition: the unique factorization of an integer $n$ into primes whose product forms $n$

## Also see

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**decomposition**