# commutative

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## com·mu·ta·tive

(kŏm′yə-tā′tĭv, kə-myo͞o′tə-tĭv)
adj.
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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## commutative

(kəˈmjuːtətɪv; ˈkɒmjʊˌteɪtɪv)
adj
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.
comˈmutatively adv
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## com•mu•ta•tive

(kəˈmyu tə tɪv, ˈkɒm yəˌteɪ tɪv)

adj.
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.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
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"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations

## commutative

[kəˈmjuːtətɪv] adjcommutativo/a
Collins Italian Dictionary 1st Edition © HarperCollins Publishers 1995
References in periodicals archive ?
In this section, we look at bijective linear operators which preserve ([epsilon], I)-rank of matrices over antinegative commutative semiring.
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.
This is the left regular band analogue of free partially commutative monoids (also called trace monoids or graph monoids [18, 14]) and of free partially commutative groups (also called right-angled Artin groups or graph groups ).
For a commutative ring R, define a simple graph called zero-divisor graph, denoted by [GAMMA](R), whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are adjacent if and only if xy = 0 in R.
We have been teaching a mathematics course in Commutative Algebra and Algebraic Geometry at Simon Fraser University since 2006.
Then, there is an induced fuzzy retraction [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that the following diagram is commutative:
Whereas all of the other virtues relate to propriety benchmarks, engendering a negative range of blame and a positive range of praise, justice--or, more specifically, commutative justice--is not a matter of propriety, but a matter of grammar.
The initial case is where both [gamma](G) and G/[C.sub.G]([gamma](G)) are commutative.
It is known (see (4) , Theorem 4) that every commutative unital locally m-pseudoconvex (5) Hausdorff algebra is simplicial.
The notion of a Euclidean module over a commutative ring as a natural extension of the Euclidean rings was studied in .

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