Structure of hereditary orders
Structure of hereditary orders
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世袭秩序的结构
DOI：
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发表时间：
1963
期刊：
影响因子：
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通讯作者：
A. Brumer
中科院分区：
文献类型：
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作者：
A. Brumer
戴德金域上的最大阶长期以来在算术中发挥着重要作用[4; 6]。最近Auslander和Goldman [1]引入了遗传序的概念，它推广了极大序的概念，在许多方面都更令人满意。Dedekind整环R的商域上的中心单代数的i阶A称为遗传的i？如果A的全局维数为1，则为order [3]。本说明的目的是宣布一个相当完整的描述世袭订单。证明和应用将在其他地方给出。提醒所有的模都是单生的和酉的。代数在其中心上是有限维的。
Maximal orders over Dedekind domains have long played an important role in arithmetic [4; 6]. Recently Auslander and Goldman [l] have introduced the concept of hereditary order, which generalizes that of maximal order and which is more satisfactory for many purposes. An i£-order A in a central simple algebra over the quotient field of the Dedekind domain R is said to be an hereditary i?-order if the global dimension of A is one [3]. The aim of this note is to announce a fairly complete description of hereditary orders. The proofs and applications will be given elsewhere. Reminder. All modules are finitely generated and unitary. Algebras are finite dimensional over their centers.