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commutative Definition

com·mu·ta·tive (kə myo̵̅o̅t′ə tiv, käm′yə tāt′iv)

adjective

  1. of commutation; involving exchange or replacement
  2. Math. of or pertaining to an operation in which the order of the elements does not affect the result, as, in addition, 3 + 2 = 2 + 3 and, in multiplication, 2 × 3 = 3 × 2

commutative Usage Examples

Modifies a noun

  • algebra: The method is similar in some respects to the treatment of non commutative algebras.
  • justice: Commutative justice has for its sphere the exchanges that can take place between two individuals.
  • ring: Much of the theory of commutative rings is motivated by the properties of the integers.
  • law: Two questions arise here: for what series the commutative law is valid; how can the sum change upon rearrangement of the terms?
  • diagram: This trick comes in handy for making commutative diagrams of diagrams like braids.
  • group: The non-zero elements of F form a commutative group.

Modifying Another Word

necessarily: Recall that in Heisenberg's first paper, he defined a multiplication which was not necessarily commutative.