A Completion of \mathbb{Z} is a Field期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A Completion of \mathbb{Z} is a Field

Authors:	J E Marcos

Institution:	(1) Departamento Algebra y Geometría, Facultad de Ciencias, 47005 Valladolid, Spain

Abstract:	We define various ring sequential convergences on $\mathbb{Z}$ and $\mathbb{Q}$ . We describe their properties and properties of their convergence completions. In particular, we define a convergence $\mathbb{L}_1$ on $\mathbb{Z}$ 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 $\mathbb{Z}/\left( p \right)$ Further, we show that $\left( {\mathbb{Z},\mathbb{L}_{_1 }^{{\kern 1pt} *} } \right)$ is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan.

Keywords:	sequential convergence convergence ring completion of a convergence ring
本文献已被 SpringerLink 等数据库收录！