论文标题
一维微分方程的流环
Ring of flows of one-dimensional differential equations
论文作者
论文摘要
在本文中，构建了积分域上的自主微分方程的流环。首先，我们构建自主环$ \ opa（\ hurw_ {r} [[x]]）$，然后研究其结构。接下来，我们构建了正式的指数生成圈的环$ \ opa（\ hurw_ {r} [[x]）$，当系统的向量字段可以在功能的总和或产品中分解时，可以在其中找到一个订单第一方程的解决方案。
In this article, the ring of flows of autonomous differential equations of order one on integral domains is constructed. First, we build the autonomous ring $\Opa(\hurw_{R}[[x]])$ and then its structure is studied. Next, we build the ring of formal exponential generating series of the ring $\Opa(\hurw_ {R} [[x]]) $, where it is possible to find solutions of differential equations of order one when the vector field of the system can be decomposed in sum or product of functions.
