On a relative uniform completion of an archimedean lattice ordered group

Mathematica Slovaca

Judita Lihová¹  Štefan Černák¹ 

关键词: Cantor extension;    relative uniform completion;    completely subdirect product;    direct factor;    basis;   

DOI  :  10.2478/s12175-009-0120-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

The notion of a relatively uniform convergence (ru-convergence) has been used first in vector lattices and then in Archimedean lattice ordered groups.Let G be an Archimedean lattice ordered group. In the present paper, a relative uniform completion (ru-completion) $$G_{omega _1 } $$ of G is dealt with. It is known that $$G_{omega _1 } $$ exists and it is uniquely determined up to isomorphisms over G. The ru-completion of a finite direct product and of a completely subdirect product are established. We examine also whether certain properties of G remain valid in $$G_{omega _1 } $$. Finally, we are interested in the existence of a greatest convex l-subgroup of G, which is complete with respect to ru-convergence.

【 授权许可】

Unknown