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.

中文翻译：

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偏斜多项式的范数

设D是其中心上的有限维除法代数，且R = D [ t ; σ , δ ] 偏斜多项式环。在δ和σ 的某些假设下，中心商环D ( t ; σ , δ ) = { f / g | f ∈ D [ t ; σ , δ ], g ∈ C ( D [ t ; σ ,δ ])} 的D [ t ; σ , δ ] 是具有约简范数N的中心简单代数。我们计算规范ñ（˚F）为一些歪斜多项式˚F ∈ [R和调查时，和的还原性如何ñ（˚F）反映的还原˚F。