Commute, commutation or commutative may refer to:
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Commuting, the process of travelling between a place of residence and a place of work
Mathematics
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Commutative property, a property of a mathematical operation whose result is insensitive to the order of its arguments
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Equivariant map, a function whose composition with another function has the commutative property
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Commutative diagram
350px, The commutative diagram used in the proof of the five lemma.
In mathematics, and especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the s ...
, a graphical description of commuting compositions of arrows in a mathematical category
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Commutative semigroup
In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists o ...
,
commutative monoid,
abelian group, and
commutative ring
In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily, noncommutative algebra is the study of ring properties that are not sp ...
, algebraic structures with the commutative property
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Commuting matrices, sets of matrices whose products do not depend on the order of multiplication
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Commutator
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory.
Group theory
The commutator of two elements, a ...
, a measure of the failure of two elements to be commutative in a group or ring
Science and technology
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Commutator (electric)
A commutator is a rotary electrical switch in certain types of electric motors and electrical generators that periodically reverses the current direction between the rotor and the external circuit. It consists of a cylinder composed of multiple ...
, a rotary switch on the shaft of an electric motor or generator
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Commutation (neurophysiology), how certain neural circuits in the brain exhibit noncommutativity
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Commutation (telemetry), a form of time-division multiplexing
* Commutation, a synonym for
packet switching in computer networking and telecommunications
Other uses
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Commutation (law) (of sentence), a reduction in severity of punishment
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Commutation (finance) (law) to lessen periodic dues (usually rents, fares or tithes) by paying a lump sum
* Commutation (finance) under a cash option,
encashment. The act of a
pension
A pension (, from Latin ''pensiō'', "payment") is a fund into which a sum of money is added during an employee's employment years and from which payments are drawn to support the person's retirement from work in the form of periodic payments ...
member/annuitant who gives up part or all in exchange for a lump sum payment.
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