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 (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.


the property of being commutative
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References in periodicals archive ?
The sample shows some understanding of commutativity and symbolic notation of multiplication, and correct number facts for 24.
Note that: Dislike the Neutrosophic crisp dilation operator, the Neutrosophic crisp erosion does not satisfy commutativity and the associativity properties.
2] has a very nice form which is the key for determining commutativity We showed
Yager's method and the method in [28] only satisfy commutativity, but not associativity.
Orders of integration are rearranged in (15) owing to the commutativity in pairs of the partial differential operators.
Based on these intuitionistic fuzzy Einstein operations and fuzzy measure, we develop some new aggregation operators, such as intuitionistic fuzzy Einstein Choquet averaging (IFCAS) operator, intuitionistic fuzzy Einstein Choquet geometric (IFCGS) operator, and study various special cases of the operators, and also investigate some desired properties of the developed operators, such as commutativity, idempotency, boundary, etc.
Wei (2010a) investigated the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionisticfuzzy numbers or interval-valued intuitionisticfuzzy numbers and proposed two new aggregation perators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator, and studied some desirable properties of the I-IFOWG and I-IIFOWG operators, such as commutativity, idempotency and monotonicity.
The commutativity of the strong product follows from the symmetry of the definition of adjacency and for associativity see [10].
The aleatory contracts represent a distinct species of contracts found in our civil law, being characterized by the alea element (dice, luck, risk, danger, hazard), representing the exceptions to the commutativity, which represents the rule in contractual matters following to which, at the conclusion of a contract, the existence and the extent of the benefits payable by the parties are clear and can be appreciated even at the time.
Moreover, several authors studied commutativity in prime and semiprime rings admitting derivations and generalized derivations which satisfy appropriate algebraic conditions on suitable subsets of the rings.
Kumar: Minimal commutativity and common fixed points, J.
They include discussions of the Galois map and its induced maps, when direct sums of modules inherit certain properties, prime rings with left derivations, some commutativity theorems concerning additive mappings and derivations on semi-prime rings, a short proof that continuous modules are clean, and imprimitive regular action in the ring of integers modulo n.