The norm of a skew polynomial

Pumpluen, Susanne; Thompson, Daniel

Abstract

Let D be a finite-dimensional division algebra over its center and R=D[t;σ,δ] a skew polynomial ring. Under certain assumptions on δ and σ, the ring of central quotients D(t;σ,δ)={f/g|f∈D[t;σ,δ],g∈C(D[t;σ,δ])} of D[t;σ,δ] is a central simple algebra with reduced norm N. We calculate the norm N(f) for some skew polynomials f∈R and investigate when and how the reducibility of N(f) reflects the reducibility of f.

• Journal Article Type: Article
• Acceptance Date: Mar 24, 2021
• Online Publication Date: Jun 15, 2021
• Publication Date: 2022-08
• Deposit Date: Mar 24, 2021
• Publicly Available Date: Jun 15, 2021
• Journal: Algebras and Representation Theory
• Print ISSN: 1386-923X
• Electronic ISSN: 1572-9079
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 4
• Pages: 869–887
• DOI: https://doi.org/10.1007/s10468-021-10051-z
• Public URL: https://nottingham-repository.worktribe.com/output/5413357
• Publisher URL: https://link.springer.com/article/10.1007/s10468-021-10051-z