$\widetilde{\mathbb{A}}_n$ II的Gabriel-Roiter测度
The Gabriel-Roiter measure for $\widetilde{\mathbb{A}}_n$ II
摘要：
设$Q$是$\widetilde{\mathbb{A}}_n$型的驯服范畴，$\Rep(Q)$是代数闭域上的有限维表示范畴.一个表示被简单地称为一个模块。它将表明，一个正规的弦模，直到同构，最多有两个加布里埃尔-罗伊特子模。具有汇-源定向的箭图$Q$将被刻画为中心部分不包含预内射模的箭图。它也将表明，只有1000多个（中央）加布里埃尔-罗伊特措施承认没有直接的前身。这一事实将被推广到所有驯服的颤抖。
英文摘要：
Let $Q$ be a tame quiver of type $\widetilde{\mathbb{A}}_n$ and $\Rep(Q)$ the category of finite dimensional representations over an algebraically closed field. A representation is simply called a module. It will be shown that a regular string module has, up to isomorphism, at most two Gabriel-Roiter submodules. The quivers $Q$ with sink-source orientations will be characterized as those, whose central parts do not contain preinjective modules. It will also be shown that there are only finitely many (central) Gabriel-Roiter measures admitting no direct predecessors. This fact will be generalized for all tame quivers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
