On a notion of "Galois closure" for extensions of rings
On a notion of "Galois closure" for extensions of rings
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DOI：
10.4171/jems/478
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
M. Bhargava;M. Satriano
中科院分区：
文献类型：
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作者：
M. Bhargava;M. Satriano
我们引入了环延拓的“伽罗瓦闭包”概念。我们表明，在域的 S_n 度 n 扩展的情况下，该概念与通常的伽罗瓦闭包概念一致。此外，我们证明了该结构的许多属性；例如，我们表明它是函数式的并且尊重基础变化。我们还研究了这种伽罗瓦闭包构造对于各种自然类别的环扩展的行为。
We introduce a notion of "Galois closure" for extensions of rings. We show that the notion agrees with the usual notion of Galois closure in the case of an S_n degree n extension of fields. Moreover, we prove a number of properties of this construction; for example, we show that it is functorial and respects base change. We also investigate the behavior of this Galois closure construction for various natural classes of ring extensions.