论文标题
环和环对固定环的性能的下降
Descent of properties of rings and pairs of rings to fixed rings
论文作者
论文摘要
让$ g $是通过戒指自动形态在整体域上行动的集团。 \σ（r）= r \ \ text {对于g \}中的所有} \σ\，$ the动作的固定环。在本文中，我们证明，在操作$ r \ rightarrow r^g：$本地pqr域，强g域，g域，希尔伯特环，$ s $ strong-strong-strong-strong戒指和根闭合域下，我们证明了以下戒指的类别。进一步，让$ \ Mathscr {p} $为环理论属性，$ r \ subseteq s $为环。一双环$（r，s）$据说是$ \ mathscr {p} $ - 一对，如果$ t $满足每个中间环$ r \ r \ subseteq t \ subseteq S. $ \ mathscr {p} $在某些情况下。例如，如果$ \ mathscr {p} = $降低，伪值域和“域中链的有限长度”，我们显示这些属性中的每一个都从$（r，s）\ rightarrow（r^g，s^g）。$成功地转移
Let $G$ be a group acting via ring automorphisms on an integral domain $R.$ A ring-theoretic property of $R$ is said to be $G$-invariant, if $R^G$ also has the property, where $R^G=\{r\in R \ | \ σ(r)=r \ \text{for all} \ σ\in G\},$ the fixed ring of the action. In this paper we prove the following classes of rings are invariant under the operation $R\rightarrow R^G:$ locally pqr domains, Strong G-domains, G-domains, Hilbert rings, $S$-strong rings and root-closed domains. Further let $\mathscr{P}$ be a ring theoretic property and $R\subseteq S$ be a ring extension. A pair of rings $(R,S)$ is said to be a $\mathscr{P}$-pair, if $T$ satisfies $\mathscr{P}$ for each intermediate ring $R\subseteq T\subseteq S.$ We also prove that the property $\mathscr{P}$ descends from $(R,S)\rightarrow (R^G, S^G)$ in several cases. For instance, if $\mathscr{P}=$ Going-down, Pseudo-valuation domain and "finite length of intermediate chains of domains", we show each of these properties successfully transfer from $(R,S)\rightarrow (R^G, S^G).$
