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On a notion of “Galois closure” for extensions of rings

Manjul BhargavaMatthew Satriano — 2014

Journal of the European Mathematical Society

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.

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