The norm of a skew polynomial

2020/06/18 by Pumpluen, Susanne, Thompson, Daniel · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2006.10418

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.

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