On a notion of "Galois closure" for extensions of rings

Details On a notion of "Galois closure" for extensions of rings On a notion of "Galois closure" for extensions of rings

2010-06-13

arxiv.org/abs/1006.2562v1

Mathematics

Commutative Algebra

28 pages

Scientific paper

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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