Classification of factorial generalized down-up algebras
St\'ephane Launois, Samuel A. Lopes
TL;DR
This paper characterizes when factorial generalized down-up algebras are Noetherian unique factorization domains or rings, providing criteria for their algebraic structure and factorization properties.
Contribution
It establishes necessary and sufficient conditions for generalized down-up algebras to be Noetherian UFDs or UFRs, advancing understanding of their algebraic properties.
Findings
Identifies conditions for Noetherian UFD status
Determines criteria for Noetherian UFR status
Provides a classification framework for these algebras
Abstract
We determine when a generalized down-up algebra is a Noetherian unique factorisation domain or a Noetherian unique factorisation ring.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models