Solvability of commutative power-associative nilalgebras of nilindex 4 and dimension

• Elgueta, Luisa ^[1] ; Suazo Delgado, Avelino ^[1]
  1. [1] Universidad de La Serena

     Universidad de La Serena

     La Serena, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 2, 2004, págs. 123-129
• Idioma: inglés
• DOI: 10.4067/S0716-09172004000200005
• Enlaces
  • Texto completo
• Resumen

  • Let A be a commutative power-associative nilalgebra. In this paper we prove that when A (of characteristic ≠2) is of dimension ≤ 8 and x⁴ = 0 for all x ∈ A, then ((A²)²)² = 0. That is, A is solvable. We conclude that if A is of dimension ≤ 7 over a field of characteristic ≠2, 3 and 5, then A is solvable.

• Referencias bibliográficas
  • Citas [1] Correa, I.; Suazo, A. On a class of commutative power-associative nilalgebras. Journal of Algebra, 215, pp. 412-417, (1999).
  • [2] Correa, I.; Hentzel I. R.; Peresi, L. A. On the solvability of the commutative power-associative nilalgebras of dimension 6. Linear Alg....
  • [3] Elgueta, L.; Suazo, A. Jordan nilalgebras of nilindex n and dimension n + 1. Communications in Algebra, 30, pp. 5547-5561, (2002).
  • [4] Elgueta, L.; Gutierrez Fernandez, J. C.; Suazo, A. Nilpotence of a class of commutative power-associative nilalgebras. Submitted.
  • [5] Gerstenhaber, M.; Myung, H.C. On commutative power-associative nilalgebras of low dimension. Proc. Amer. Math. Soc., 48, pp. 29-32, (1975).
  • [6] Gutierrez Fernandez J.C. On commutative power-associative nilalgebras. Communications in Algebra, 32(6), pp. 2243-2250, (2004).
  • [7] Schafer, R.D. An Introduction to Nonassociative Algebras; Academic Press: New York/London, (1966).
  • [8] Suttles, D.A. Counterexample to a conjeture of Albert. Notices Amer. Math. Soc. , 19, A-566, (1972).
  • [9] Zhevlakov, K.A.; Slinko, A.M.; Shestakov, I.P.; Shirshov, A.I. Rings That Are Nearly Associative; Academic Press: New York/London, (1992).