A note on derivations of commutative algebras

@inproceedings{Anderson1966ANO,
  title={A note on derivations of commutative algebras},
  author={T. Anderson},
  year={1966}
}
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
9 Citations
A Generalization of Noncommutative Jordan Algebras*
  • Highly Influenced
  • PDF
On nearly commutative nodal algebras in characteristic zero
  • PDF
Flexible Lie-admissible algebras
  • 29
Nearly associative deformation quantization
  • 5
  • PDF
Algebras satisfying congruence relations
  • PDF
On generalizations of alternative algebras.
  • PDF
Varieties of algebras
  • 81

References

SHOWING 1-9 OF 9 REFERENCES
Commutative algebras satisfying an identity of degree four
  • 32
  • PDF
A generalization of alternative rings
  • 9
  • PDF
On an identity common to Lie, Jordan, and quasi-associative algebras, Ph.D
  • 1964
Flexible algebras of degree one
  • 8
  • PDF
Lie algebras, I nterscience
  • New York,
  • 1962
On Nilalgebras and Linear Varieties of Nilpotent Matrices, I
  • 89
A theory of power-associative commutative algebras
  • 87
  • PDF