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-commutat...

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Autores:: Hernández Mogollón, Jason Ricardo

Tipo de recurso:

Fecha de publicación:: 2019

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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Summary:	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.

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

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