A note on derivations of commutative algebras

  title={A note on derivations of commutative algebras},
  author={T. Anderson},
It is well known that the (solvable) radical of a Lie or Jordan algebra is invariant under all derivations of the algebra if the groundfield is not modular [4] and [5]. In this note we obtain a similar result for commutative power-associative algebras of degree one by following Jacobson's argument in [5] and then appealing to a theorem of Gerstenhaber [3] at that point where the Jordan identity was required. Our result (Theorem 1) seems useful in classifying simple algebras of degree one which… Expand
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