Link graphs of tiled orders over a local Dedekind domain
Link graphs of tiled orders over a local Dedekind domain
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本地 Dedekind 域上平铺订单的链接图
DOI：
10.21099/tkbjm/1496160459
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发表时间：
1986
影响因子：
0.7
通讯作者：
H. Fujita
中科院分区：
文献类型：
--
作者：
H. Fujita
令 R 为具有最大理想 nR 和商环 K 的局部 Dedekind 域，并令 A = (Aij) 为 (R)n 和 (nR)n 之间 (R)nDA D (nR)n 之间 (K)n（if 上的 fulln x n 矩阵环）中的瓦片阶。在[2，定理]中，我们得到了根据i?/7ri?-代数A=A/(nR)n的颤动确定A的链接图的过程。如[2，备注（4）]中所述，存在具有相同链接图的tiledi？-阶A和/”，但A=A/(nR)n的颤动与B=r/(nR)n的颤动不同。在本注释中，我们将通过证明以下内容来澄清这样的A和F之间的关系
Let R be a local Dedekind domain with the maximal ideal nR and the quotient ring K, and let A = (Aij) be a tiledi?-order in (K)n (the fulln x n matrix ring over if) between (R)n and (nR)n (i.e.,(R)nDA D (nR)n). In [2, Theorem], we have obtained a procedure of determining the link graph of A from the quiver of the i?/7ri?-algebra A =A/(nR)n. As noted in [2, Remark (4)], there exist tiledi?-orders A and /"with the same link graph, but the quiver of A=A/(nR)n is different from that of B=r/(nR)n. In this note, we shall clarify the relationship between such A and F, by proving the following