Definition:Decomposition

Disambiguation

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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

• Definition:Decomposable
• Definition:Composition
• Definition:Composite

Sources

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