International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 24, Pages 4041-4048
doi:10.1155/IJMMS.2005.4041

Compatible elements in partly ordered groups

Jiří Močkoř1 and Angeliki Kontolatou2

 1Department of Mathematics, University of Ostrava, Ostrava CZ-702 00, Czech Republic
2Department of Mathematics, School of Natural Sciences, University of Patras, Patras 26500, Greece
Received 16 September 2004; Revised 28 September 2005

Abstract

Some conditions equivalent to a strong quasi-divisor property (SQDP) for a partly ordered group G are derived. It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal is generated by two elements. A topological density condition in topological group of finitely generated t-ideals and/or compatible elements are proved to be equivalent to SQDP.