论文标题
关于稳定域的算术
On the arithmetic of stable domains
论文作者
论文摘要
如果每个非零的理想$ i $ r $ $ r $都在其内态戒指上投影，则通勤环$ r $是稳定的。从1960年代，稳定的戒指在1960年代的动机上引起了人们的关注。在稳定戒指的代数结构以及稳定性与其他代数属性（例如分区和$ 2 $生成器属性）的关系上，众所周知。在本文中，我们研究了稳定积分域的算术，重点是Dedekind域中稳定订单理想的半群的算术特性。
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.
