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A completion of is a field

José E. Marcos (2003)

Czechoslovak Mathematical Journal

We define various ring sequential convergences on and . We describe their properties and properties of their convergence completions. In particular, we define a convergence 𝕃 1 on by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields / ( p ) . Further, we show that ( , 𝕃 1 * ) is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.

A monogenic Hasse-Arf theorem

James Borger (2004)

Journal de Théorie des Nombres de Bordeaux

I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.

Adic-completion and some dual homological results.

Anne-Marie Simon (1992)

Publicacions Matemàtiques

Let a be an ideal of a commutative ring A. There is a kind of duality between the left derived functors Uia of the a-adic completion functor, called local homology functors, and the local cohomology functors Hai.Some dual results are obtained for these Uia, and also inequalities involving both local homology and local cohomology when the ring A is noetherian or more generally when the Ua and Ha-global dimensions of A are finite.

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