Gelfand-Kirillov Dimension and Local Finiteness of Symmetrizations of Associative: superalgebras

• Autores: Esther García
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 145, Nº 3, 2005, págs. 229-238
• Idioma: alemán
• DOI: 10.1007/s00605-005-0314-3
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• Resumen

  • In this work we extend to superalgebras a result of Skosyrskii [Algebra and Logic, 18 (1) (1979) 49¿57, Lemma 2] relating associative and Jordan structures. As an application, we show that the Gelfand-Kirillov dimension of an associative superalgebra coincides with that of its symmetrization, and that local finiteness is equivalent in associative superalgebras and in their symmetrizations. In this situation we obtain that having zero Gelfand-Kirillov dimension is equivalent to being locally finite.