# commutative

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## com·mu·ta·tive

(kŏm′yə-tā′tĭv, kə-myo͞o′tə-tĭv)
1. Relating to, involving, or characterized by substitution, interchange, or exchange.
2. 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.

com·mu′ta·tiv′i·ty (kə-myo͞o′tə-tĭv′ĭ-tē) n.

## commutative

(kəˈmjuːtətɪv; ˈkɒmjʊˌteɪtɪv)
1. relating to or involving substitution
2. (Mathematics) maths logic
a. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
b. relating to this property: the commutative law of addition.
3. (Logic) maths logic
a. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
b. relating to this property: the commutative law of addition.

## com•mu•ta•tive

(kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪv)

1. of or pertaining to commutation, exchange, substitution, or interchange.
2.
a. (of a binary operation) having the property that one term operating on a second is equal to the second operating on the first, as axb=bx a.
b. having reference to this property: the commutative law for multiplication.
[1525–35; < Medieval Latin]
com•mu`ta•tiv′i•ty, n.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Adj. 1 commutative - (of a binary operation) independent of order; as in e.g. "a x b = b x a"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementindependent - free from external control and constraint; "an independent mind"; "a series of independent judgments"; "fiercely independent individualism"
Translations

## commutative

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The semisimple Hopf algebra kG* is commutative and the elements {[p.
is a commutative neutrosophic quadruple ring called a neutrosophic quadruple ring of integers modulo n.
Matching Protocol Based on Commutative Encryption Function.
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The current money and banking system also violates commutative justice (justice in exchange) through the institutionalization of usury.
CoCoATeam CoCoA: a system for doing Computations in Commutative Algebra Available at http://cocoa.
In Section 3, we look at bijective linear preservers of ([epsilon], I)-rank for all matrices over commutative antinegative semirings.
In The Theory of Moral Sentiments, he describes several types of justice, but commutative justice--abstaining from directly harming another--is most important:
On the margins of the meeting, the governor of the Bank of Korea accompanied by the governor of the central bank visited the central bank's Museum which includes part of the central bank's collection of currency notes, currency coins, commutative coins, gifts, samples of issued UAE currency notes/coins and currencies of other countries, in addition to cash counting and sorting machines that were used by the Central Bank in the past.
Readers should have a background in number theory, commutative algebra, and the general theory of schemes.

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