On the smoothness of 3-dimensional skew polynomial rings
Andr\'es Rubiano, Armando Reyes
TL;DR
This paper investigates the differential smoothness of 3-dimensional skew polynomial rings, expanding understanding of their algebraic properties within noncommutative geometry.
Contribution
It provides a detailed analysis of the differential smoothness of a specific family of 3D skew polynomial rings, a topic not previously explored in depth.
Findings
Established conditions for differential smoothness of these rings
Identified classes of skew polynomial rings with smooth differential structures
Extended the theory of noncommutative differential geometry
Abstract
This paper is part of a series of papers in which we have investigated the differential smoothness of families of noncommutative algebras. Here, we consider this topic for the family 3-dimensional skew polynomial rings characterized by Bell and Smith \cite{BellSmith1990}.
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Taxonomy
TopicsRings, Modules, and Algebras · Polynomial and algebraic computation · Algebraic structures and combinatorial models