Abstract
In this paper, we give a new generalization of metric spaces called k-metric spaces. Our k-metrics are valued in lattice ordered groups, which allows us to talk about distance in non-abelian lattice ordered groups. We also discuss a class of (not necessarily abelian) lattice ordered groups in which every k-metric induces a topology. Then we show that every k-metric valued in the real numbers is metrizable. In the last section, we characterize intrinsic metrics on lattice ordered rings that are almost f-rings and prove that being an almost f-ring is necessary and sufficient for this characterization. Then we show that if a lattice ordered ring is representable, then every intrinsic metric is a k-metric.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
