On a relative uniform completion of an archimedean lattice ordered group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

On a relative uniform completion of an archimedean lattice ordered group

Authors:	Štefan Černák Judita Lihová

Affiliation:	(1) Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01 Košice, Slovakia;(2) Institute of Mathematics, P. J. Šafárik University, Jesenná 5, SK-041 54 Košice, Slovakia;(3) Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, SK-040 01 Košice, Slovakia

Abstract:	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. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by Grant VEGA 1/3003/06.

Keywords:	Cantor extension relative uniform completion completely subdirect product direct factor basis
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