Separating invariants

• Autores: Gregor Kemper
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 9, 2009, págs. 1212-1222
• Idioma: inglés
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• Resumen

  • This paper studies separating subsets of an invariant ring or, more generally, of any set consisting of functions. We prove that a subset of a finitely generated algebra always contains a finite separating subset. We also show that a general version of Noether's degree bound holds for separating invariants, independently of the characteristic. While the general finiteness result is non-constructive, the Noether bound provides an easy algorithm for computing separating invariants of finite groups. The paper also contains a conceptual investigation of the difference between separating and generating subsets.