International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 4041-4048
Compatible elements in partly ordered groups
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
Copyright © 2005 Jiří Močkoř and Angeliki Kontolatou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Some conditions equivalent to a strong quasi-divisor property
(SQDP) for a partly ordered group are derived. It is proved that if is defined by a family of -valuations of finite character, then admits an SQDP if and only if it admits a
quasi-divisor property and any finitely generated -ideal is generated by two elements. A topological density condition in
topological group of finitely generated -ideals and/or compatible elements are proved to be equivalent to SQDP.