An example of a normal local ring which is analytically reducible
An example of a normal local ring which is analytically reducible
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解析可约的普通局部环的示例
DOI：
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发表时间：
1958
期刊：
影响因子：
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通讯作者：
M. Nagata
中科院分区：
文献类型：
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作者：
M. Nagata
作者在文献[2 ]中给出了正规局部环是解析分歧的一个例子。在这个例子中，它的完备化的零理想是准素理想。本文给出了一个正规局部环，使得它的完备化的零理想不是准素的，这是作者[3]的一个问题的反例。我们将在这里注意到，我们的例子是秩为2的正则局部环的有限可分积分扩张，它包含一个特征可能为零的域k：我们将在f k的特征不同于2的假设下构造一个例子。应当注意，即使在特性2的情况下，也可以通过对我们的示例进行轻微修改来容易地给出类似的示例。
Previously the writer [2 ] gave an example of a normal local ring which is analytically ramified. In that example, the zero ideal o f its completion is a primary ideal. In the present note, we shall show a normal local ring such that the zero ideal o f its completion is not primary, which gives a counter example to a problem of the writer [3]. We shall remark here that our example is a finite separable integral extension of a regular local ring of rank 2 which contains a field k whose characteristic may be zero : we shall construct an example under th e assumption that the characteristic o f k is different from 2. It should be noted that even in the case of characteristic 2, a similar example can be given easily by a slight modification of our example.