论文标题
偏斜多项式的规范
The norm of a skew polynomial
论文作者
论文摘要
令$ d $是其中心上方的有限维划分代数，$ r = d [t;σ，δ] $ a偏斜多项式环。在$δ$和$σ$的某些假设下，中央商环$ d（t;σ，δ）= \ {f/g \，| \，| \，f \，in d [t;σ，δ]，g \ in c（d [t;σ，δ，δ]）\ d [t;σ，δ]）\ d;我们计算一些偏斜多项式$ f \ in r $的norm $ n（f）$，并调查$ n（f）$的降低性何时以及如何反映$ f $的降低性。
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 $D(t;σ,δ) = \{f/g \,|\, f \in D[t;σ,δ], g \in C(D[t;σ,δ])\}$ of $D[t;σ,δ]$ is a central simple algebra with reduced norm $N$. We calculate the norm $N(f)$ for some skew polynomials $f\in R$ and investigate when and how the reducibility of $N(f)$ reflects the reducibility of $f$.
