The Hilbert's Nullstellensatz over skew Poincaré-Birkhoff-Witt extensions

In this work we study several versions of the Hilbert's Nullstellensatz. We begin with a commutative review of its geometric interpretation following the study of affine and projective case. Later, we consider its algebraic interpretation. Next, we present several treatments to the non-commutative interpretation. Therefore, we begin with Ore extensions, their properties and obstructions with classical methods. We consider a relationship between the Hilbert's Nullstellensatz and the notion of generic flatness. Subsequently we use the filtration-graduation technique over almost normalizing extensions (also called almost commutative algebras) with the aim of state a theorem that helps us to guarantee conditions such that the Hilbert's Nullstellensatz holds. Finally, we study skew Poincaré-Birkhoff-Witt extensions together with some of their homological and ring-theoretical properties in order to extend Hilbert's Nullstellensatz to such extensions.

• Autores: Hernández Mogollón, Jason Ricardo
• Fecha de publicación: 2019
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/77035
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/77035; http://bdigital.unal.edu.co/74233/
• Palabra clave: Hilbert's Nullstellensatz; Skew PBW extension; Jacobson ring; Generic flatness; Anillo de Jacobson; Planitud genérica
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional