Contracted ideals from integral extensions of regular rings
Contracted ideals from integral extensions of regular rings
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规则环整体延伸的收缩理想
DOI：
10.1017/s0027763000015701
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发表时间：
1973
影响因子：
0.8
通讯作者：
M. Hochster
中科院分区：
文献类型：
--
作者：
M. Hochster
0.导论.本文考虑了如下问题：若R是正则Noether环，S ∈ R是模有限R-代数，R是否是S作为R-模的直和项？当R包含域时，给出了肯定的回答，并证明了当S的局部环的完备化具有[6] § 1意义下的极大Cohen-Macaulay模时，结论在这种情况下也成立.因此，如果[6]的猜想E为真，那么这里提出的问题就有了肯定的答案，而不需要对正则诺特环R作进一步的限制，并且这里将表明，只需要猜想E的一个大大削弱的版本。
0. Introduction. The purpose of this paper is to consider the following question: if R is a regular Noetherian ring and S ⊃ R is a module-finite R-algebra, is R a direct summand of S as R-modules? An affirmative answer is given if R contains a field, and it is shown that if the completions of the local rings of S possess maximal Cohen-Macaulay modules in the sense of § 1 of [6] then the conclusion is valid in this case too. Hence, if Conjecture E of [6] is true then the question raised here has an affirmative answer without further restriction on the regular Noetherian ring R, and it will be shown here that only a greatly weakened version of Conjecture E is needed.