The Norm of a Skew Polynomial
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AbstractLet 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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2017 ◽
Vol 154
(2)
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pp. 410-458
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2015 ◽
Vol 14
(04)
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pp. 1550048
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2021 ◽
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pp. 75-89
2010 ◽
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pp. 921-932
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pp. 6-26
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1980 ◽
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pp. 483-493
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