commutator
Sign in to saveIn 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.
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Encyclopedic overview
15 sectionsContents
- Group theory
- Identities (group theory)
- Ring theory
- Identities (ring theory)
- Lie-algebra identities
- Additional identities
- Exponential identities
- Graded rings and algebras
- Adjoint derivation
- General Leibniz rule
- See also
- Notes
- References
- Further reading
- External links
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, and , of a group , is the element .
Excerpted from Wikipedia’s “commutator” article, available under the CC BY-SA 4.0 licence.