Algebra theory MOC

Derivation on an algebra

A derivation on an algebra over a field is a linear endomorphism satisfying the product rule #m/def/ralg

for all . One can more generally define a derivation for any -bimodule .

Properties

  1. The commutator of two derivations is itself a derivation
  2. A derivation on a -monoid is a derivation on its commutator
Proof of 2

Let be a unital associative algebra over and be a derivation of . Then for any

proving ^P2.

#state/tidy | #lang/en | #SemBr