论文标题
以$ \ mathbb q [x] $的离散有序的主体理想子环在离散订购的主体理想子环中控制质量序列的分布
Controlling distribution of prime sequences in discretely ordered principal ideal subrings of $\mathbb Q[x]$
论文作者
论文摘要
我们展示了如何使用各种类型的主要行为构建$ \ mathbb q [x] $的离散订购的主要理想子环。给定任何设置的$ \数学d $由有限增加的序列$（d_1，d_2，\ dots，d_l）$的正整数$，以至于对于每个Prime Integer $ p $ $ p $，我们可以规定，对于每个$（d_1，\ dots，d_l）\ in \ Mathcal d $，是一组pressconions $（F，F，F+D_1，\ d_1，f+d_l）$ prime元素的cofinal集合。此外，我们可以同时保证r_τ\ setminus \ mathbb n $中的每个正质量$ g \要么在上述规定的进度中，要么在$r_τ$中没有其他prime $ h $，因此$ g-h \ in \ mathbb z $。最后，我们因此构建的所有主要理想域都是非欧洲裔和同构的，与pofinite Integers的环$ \ hat {\ mathbb {z}} $的子环。
We show how to construct discretely ordered principal ideal subrings of $\mathbb Q[x]$ with various types of prime behaviour. Given any set $\mathcal D$ consisting of finite strictly increasing sequences $(d_1,d_2,\dots, d_l)$ of positive integers such that, for each prime integer $p$, the set $\{p\mathbb Z, d_1+p\mathbb Z,\dots, d_l+p\mathbb Z\}$ does not contain all the cosets modulo $p$, we can stipulate to have, for each $(d_1,\dots, d_l)\in \mathcal D$, a cofinal set of progressions $(f, f+d_1, \dots, f+d_l)$ of prime elements in our principal ideal domain $R_τ$. Moreover, we can simultaneously guarantee that each positive prime $g\in R_τ\setminus\mathbb N$ is either in a prescribed progression as above or there is no other prime $h$ in $R_τ$ such that $g-h\in\mathbb Z$. Finally, all the principal ideal domains we thus construct are non-Euclidean and isomorphic to subrings of the ring $\hat{\mathbb{Z}}$ of profinite integers.
