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On the smoothness of 3-dimensional skew polynomial rings

Andrés Rubiano, Armando Reyes

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}.

On the smoothness of 3-dimensional skew polynomial rings

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}.
Paper Structure (7 sections, 5 theorems, 69 equations, 1 table)

This paper contains 7 sections, 5 theorems, 69 equations, 1 table.

Table of Contents

  1. Introduction
  2. Definitions and Preliminaries
  3. Differential smoothness of algebras
  4. 3-dimensional skew polynomial algebras
  5. Differential and integral calculus
  6. Future work
  7. Declarations

Key Result

Proposition 2.5

Let $(\Omega A, d)$ be an $n$-dimensional differential calculus over an algebra $A$. The following assertions are equivalent:

Theorems & Definitions (17)

  • Definition 2.1: BrzezinskiSitarz2017
  • Definition 2.2: Brzezinski2008
  • Definition 2.3: Brzezinski2008
  • Definition 2.4: BrzezinskiSitarz2017
  • Proposition 2.5: BrzezinskiSitarz2017
  • Proposition 2.6
  • Definition 2.7: BrzezinskiSitarz2017
  • Proposition 2.8: Rosenberg1995
  • Remark 2.9
  • Example 2.10
  • ...and 7 more