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

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Armando Reyes https://orcid.org/0000-0002-5774-0822
Jason Hernández-Mogollón


Hilbert’s Nullstellensatz, skew PBW extension, Jacobson ring, generic flatness


In 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 Poincaré-Birkhoff-Witt extensions. Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry. 


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