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{{r|Commutativity}}

If ''x'' and ''y'' [[commutativity|commute]] then the conjugate of ''x'' by ''y'' is just ''x'' again. The [[

The notion of ''commutative [[ring (mathematics)|ring]]'' assumes commutativity of the multiplication operation and usually the existence of a multiplicati

The second and third axioms imply commutativity: it is possible (but not easy) to show that in the presence of the other th

#<b>A</b> • <b>B</b> = <b>B</b> • <b>A</b> (commutativity or symmetry)

...arithmetic is surprisingly straightforward. The main difficulty is that [[commutativity]] in multiplication is lost &mdash; for two quaterions ''q''₁ an They are a [[Commutativity|non-commutative]] extension of the real numbers. They were first described

* [[Commutativity]]: <math>x \vee y = y \vee x;~ x \wedge y = y \wedge x ;\,</math>

* If ''R'' is [[commutativity|commutative]] then so is ''R''[''X''].

;[[Commutativity]]

...ar, in [[Quantum mechanics]], the [[Heisenberg equation]] deals with non-[[commutativity|commuting]] objects ([[operator (quantum mechanics)|operator]]s).

...ration|Commutativity]]''': Addition of integers also has a property called commutativity. That is, the order of the numbers to be added does not affect the sum. For If a group is also [[commutativity|commutative]] - that is, for any two members ''a'' and ''b'' of ''S'', ''a'

| [[commutativity]]: || ''a''&nbsp;+&nbsp;''b''&nbsp;&nbsp;=&nbsp;&nbsp;''b''&nbsp;+&nbsp;''a

* [[Commutativity]]: <math>x \vee y = y \vee x;~ x \wedge y = y \wedge x ;\,</math>

...tic curve <math>E</math> is defined as <math>p+q:=O*(p*q)</math>. Both the commutativity and the existence of inverse follow from the definition. The proof of the a

Just as with numeric addition, matrix addition is [[commutativity|commutative]]:

The operation in a group need not be [[commutativity|commutative]], that is there may exist elements ''a'',''b'' such that ''a''

...end on the order of terms;<ref>that is, the addition (multiplication) is [[commutativity|commutative]]</ref> the sum (product) of three or more elements does not de

...end on the order of terms;<ref>that is, the addition (multiplication) is [[commutativity|commutative]]</ref> the sum (product) of three or more elements does not de

...OD Record, 18(2), 399-407</ref> Li & Li<ref name=Li>Li, R. & Li, D. (2005) Commutativity-based concurrency control in groupware. In, International Conference on Col