Burchnall-Chaundy theory for Ore extensions
Johan Richter
TL;DR
This paper reviews classical algebraic dependence results for Weyl algebras and extends these findings to broader classes of Ore extensions, including new theoretical insights.
Contribution
It generalizes the Burchnall-Chaundy theory to various Ore extensions, adding new results to existing literature.
Findings
Classical dependence results for Weyl algebras reviewed
Generalizations to other Ore extensions described
New theoretical results on algebraic dependence established
Abstract
We begin by reviewing a classical result on the algebraic dependence of commuting elements in Weyl algebras. We proceed by describing generalizations of this result to various classes of Ore extensions, both results that have already been published and a new result.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons