Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Relating to, involving, or characterized by substitution, interchange, or exchange.
 adj. Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If a × b = b × a, the operation indicated by × is commutative.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Such that the order in which the operands are taken does not affect their image under the operation.
 adj. Having a commutative operation.
 adj. Such that any two sequences of morphisms with the same initial and final positions compose to the same morphism.
from the GNU version of the Collaborative International Dictionary of English
 adj. Relative to exchange; interchangeable; reciprocal.
 adj. having the property of commutativity.
from The Century Dictionary and Cyclopedia
 Relating to exchange; interchangeable; mutual: as, commutative justice (that is, justice which is mutually done and received).
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. (of a binary operation) independent of order; as in e.g.
Etymologies
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Examples

The market is subject to the principles of socalled commutative justice, which regulates the relations of giving and receiving between parties to a transaction.

This is justice in exchange, or what Aristotle called commutative or corrective justice.

Among equals, it is called commutative justice, the which alone is here in question.
Explanation of Catholic Morals A Concise, Reasoned, and Popular Exposition of Catholic Morals

Hence all these actions belong to the one same species of justice, namely commutative justice.

The rational numbers form what mathematicians call a commutative group under addition.

WriteaThon is Wednesday, November 5th! commutative  abelian groups are also known as commutative groups

30 That justice called commutative commands sacred respect for the division of possessions and forbids invasion of others' rights through the exceeding of the limits of one's own property; but the duty of owners to use their property only in a right way does not come under this type of justice, but under other virtues, obligations of which "cannot be enforced by legal action."

I flunked out of University three times, by which time I had a commutative average of about 53%.

This is a classic problem  human beings expect every rational statement to be commutative.

Maybe it's not a commutative property: Lean — Berlioz, but not necessarily Berlioz — Lean.
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