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espanolEn este articulo presentamos un estudio sobre algunas caracterizaciones algebraicas del teorema de Nullstellensatz de Hilbert para anillos no conmutativos de tipo polinomial. Utilizando varios resultados establecidos en la literatura, obtuvimos una version de este teorema para las extensiones de Poincare-Birkhoff-Witt. Una vez hecho esto, ilustramos el Nullstellensatz con ejemplos que aparecen en la teoria de los anillos no conmutativa y en la geometria algebraica no conmutativa. EnglishIn this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew Poincare-Birkhoff-Witt extensions. Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry.

A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type