The direct summand conjecture in dimension three
The direct summand conjecture in dimension three
复制标题
第三维的直接被加数猜想
DOI：
10.2307/3597204
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发表时间：
2002
影响因子：
4.9
通讯作者：
R. Heitmann
中科院分区：
文献类型：
--
作者：
R. Heitmann
直和项猜想断言，如果R是正则局部环，S是包含R的模有限R-代数，则R是S作为R-模的直和项。以前已知如果R包含一个域或如果dim R至多为2，则为真。本文证明了三维混合特征环的结果。证明是通过证明正闭包的扩展在三维中具有结肠捕获属性来完成的。
The direct summand conjecture asserts that if R is a regular local ring and S is a module-finite R-algebra containing R, then R is a direct summand of S as an R-module. It was previously known to be true if R contains a field or if dim R is at most two. In this article, the result is demonstrated for mixed characteristic rings of dimension three. The proof is accomplished by showing that an extension of plus closure has the colon-capturing property in dimension three.