Abstract

A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.

中文翻译：

---

关于稳定域的算术

摘要

如果R的每个非零理想I在其自同态环上射影，则交换环R是稳定的。受 1960 年代 Bass 的一篇论文的启发，稳定环从此在文献中受到广泛关注。关于稳定环的代数结构以及稳定性与其他代数性质（如除数性和 2-生成子性质）的关系，我们已经知道很多。在本文中，我们研究了稳定积分域的算术，重点是 Dedekind 域中稳定阶理想半群的算术性质。