P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
On a notion of “Galois closure” for extensions of rings
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 degree 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.
Continuous functions on compact subsets of local fields
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