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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Presented by: Kenneth Goodearl
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Pumplün, S., Thompson, D. The Norm of a Skew Polynomial. Algebr Represent Theor 25, 869–887 (2022). https://doi.org/10.1007/s10468-021-10051-z
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DOI: https://doi.org/10.1007/s10468-021-10051-z