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A completion of $ℤ$ is a field

José E. Marcos — 2003

Czechoslovak Mathematical Journal

We define various ring sequential convergences on $ℤ$ and $ℚ$ . We describe their properties and properties of their convergence completions. In particular, we define a convergence $𝕃_{1}$ on $ℤ$ 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 $ℤ / (p)$ . Further, we show that $(ℤ, 𝕃_{1}^{*})$ is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.

The algebraic closure of a $p$ -adic number field is a complete topological field

José E. Marcos — 2006

Mathematica Slovaca

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A completion of ℤ is a field

The algebraic closure of a p -adic number field is a complete topological field

A completion of $ℤ$ is a field

The algebraic closure of a $p$ -adic number field is a complete topological field