We begin by recalling the role that weak proregularity of an ideal in a commutative ring has in derived completion and adic flatness. We also introduce the new concepts of idealistic and sequential derived completion, and prove a few results about them, including the fact that these two concepts agree iff the ideal is weakly proregular. Next we study the local nature of weak proregularity, and its behavior w.r.t. ring quotients. These results allow us to prove our main theorem, which states that weak proregularity occurs in the context of bounded prisms. Prisms belong to the new groundbreaking theory of perfectoid rings, developed by Scholze and his collaborators. Since perfectoid ring theory makes heavy use of derived completion and adic flatness, we anticipate that our results shall help simplify and improve some of the more technical aspects of this theory.

我们首先回顾一下换向环中理想的弱正则性在导出的完成度和adic平坦度中所起的作用。我们还介绍了理想主义和顺序派生完成的新概念，并证明了有关它们的一些结果，包括以下两个事实：如果理想是弱规则的，则这两个概念是一致的。接下来，我们研究弱规则性的局部性质及其与环商的关系。这些结果使我们能够证明我们的主要定理，该定理指出，在有界棱柱体的情况下会发生弱的前正则性。棱镜属于新的突破性理论。Scholze和他的合作者开发的perfectoid戒指。由于Perfectoid环理论大量使用了导出的完成度和Adic平坦度，因此我们预计我们的结果将有助于简化和改进该理论的某些技术性方面。