On the invariance of subspaces in some baric algebras

• Basso, I. ^[1] ; Costa, R. ^[2] ; Picanco, J. ^[3]
  1. [1] Universidad del Bío-Bío

     Universidad del Bío-Bío

     Comuna de Concepción, Chile

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
  3. [3] Universidad Federal de Pará

     Universidad Federal de Pará

     Brasil

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 22, Nº. 1, 2003, págs. 91-102
• Idioma: inglés
• DOI: 10.4067/S0716-09172003000100006
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• Resumen

  • In this article, we look for invariance in commutative baric algebras (A, ω) satisfying (x 2 ) 2 = ω(x)x 3 and in algebras satisfying (x 2 ) 2 = ω(x 3 )x, using subspaces of kernel of ω that can be obtained by polynomial expressions of subspaces Ue e Ve of Peirce decomposition A = Ke ⊕ Ue ⊕ Ve of A, where e is an idempotent element. Such subspaces are called p -subspaces. Basically, we prove that for these algebras, the p -subspaces have invariant dimension, besides that, we find out necessary and sufficient conditions for the invariance of the p-subspaces.

• Referencias bibliográficas
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