On Sylvester Rank Functions
On Sylvester Rank Functions
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关于西尔维斯特秩函数
DOI：
10.1112/jlms/s2-43.2.199
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发表时间：
1991
影响因子：
1.2
通讯作者：
S. Westreich
中科院分区：
文献类型：
--
作者：
S. Westreich
一个非常有趣的一套定理表示环的斜领域是斯科菲尔德的理论，特点同态从任意K代数A到一个简单的artinian环，在秩函数的投射模的A。证明是基于这样一个事实，即环A U K Mn（K）有一个秩函数取值于Z/n。但是，环的余积合并一个半单Artin子环具有相当复杂的结构，斯科菲尔德的证明利用了这一点。本文在对环上模的仔细分析的基础上，给出了证明部分斯科菲尔德定理的一种简单方法
One very interesting set of theorems about representation of rings over skew fields is Schofield's theory, characterizing homomorphisms from an arbitrary K algebra A to a simple artinian ring, in terms of rank functions on the projective modules of A. The proof is based on the fact that the ring A U K Mn (K) has a rank function taking values in Z/n. But the coproduct of rings amalgamating a semisimple artinian subring has a rather complicated structure, which is utilized in Schofield's proof. In this paper we want to introduce a simpler way of proving parts of Schofield's theorems, based on a careful analysis of modules over the ring