Definition:Commutator/Ring
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Definition
Let $\struct {R, +, \circ}$ be a ring.
Let $a, b \in R$.
The commutator of $a$ and $b$ is the operation:
- $\sqbrk {a, b} := a \circ b + \paren {-b \circ a}$
or more compactly:
- $\sqbrk {a, b} := a \circ b - b \circ a$
Also see
- Results about ring commutators can be found here.
Sources
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): commutator