论文标题
在$ g（a）上_ \ mathbb {q}有限表示的戒指
On $G(A)_\mathbb{Q}$ of rings of finite representation type
论文作者
论文摘要
令$（a，\ mathfrak {m}）$为有限代表类型的本地戒指。 如果$ a $的Ar-quiver是知道的，那么根据Auslander和Reiten的结果，可以阐明$ g（a）$ Grothendieck Grothendieck Grotity of Ficalbility生成的$ A $ Modules。如果不知道ar-quiver，则在本文中，我们给出$ g（a）_ \ mathbb {q} = g（a）\ otimes_ \ mathbb {z} \ mathbb {q} $时，当$ k = a/\ mathfrak {m} $非常完美。作为一个应用程序，我们证明，如果$ a $是一种出色的等电性henselian gornstein gornstein local Ring，则具有$ \ text {char} \ a/\ mathfrak {m} \ neq 2,3,5 $（和$ a/\ a/\ mathfrak {m} $ peftss），然后\ mathbb {q} $。
Let $(A,\mathfrak{m})$ be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of $A$ is known then by a result of Auslander and Reiten one can explicity compute $G(A)$ the Grothendieck group of finitely generated $A$-modules. If the AR-quiver is not known then in this paper we give estimates of $G(A)_\mathbb{Q} = G(A)\otimes_\mathbb{Z} \mathbb{Q}$ when $k = A/\mathfrak{m}$ is perfect. As an application we prove that if $A$ is an excellent equi-characteristic Henselian Gornstein local ring of positive even dimension with $\text{char} \ A/\mathfrak{m} \neq 2,3,5$ (and $A/\mathfrak{m}$ perfect) then $G(A)_\mathbb{Q} \cong \mathbb{Q}$.
