Simplicity of noncommutative Dedekind domains

Every abelian group is the class group of a simple Dedekind domain

A classical result of Claborn states that every abelian group is the class group of a commutative Dedekind domain. Among noncommutative Dedekind prime rings, apart from PI rings, the simple Dedekind domains form a second important class. We show that every abelian group is the class group of a noncommutative simple Dedekind domain. This solves an open problem stated by Levy and Robson in their recent monograph on hereditary Noetherian prime rings.

斜洛朗级数环在戴德金整环上的研究

Skew Laurent Series Ring Over a Dedekind Domain

本文证明交换戴德金整环上的斜洛朗级数环是非交换戴德金整环，并在自同构平凡作用于理想类群时给出其K_0群同构及维数、秩等不变量。

分解与转移：超越交换性的非唯一分解

Divide and Transfer: Non-Unique Factorizations Beyond Commutativity

本文研究非交换Dedekind素环中的非唯一分解问题，通过模论方法和图示计算探讨除数理论与转移同态的应用。

戴德金超环与相关概念

Dedekind Superrings and Related Concepts

本文研究戴德金超环及相关概念，在超交换超环范畴内探讨其性质及与经典交换框架的差异。