$L$Ordered and $L$Lattice Ordered Groups
Abstract
This paper pursues an investigation on groups equipped with an $L$ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$ordered set, the notion of an $L$lattice is introduced and some related results are obtained. Then we applied them to define an $L$lattice ordered group. We also introduce convex $L$subgroups to construct a quotient $L$ordered group. At last, a relation between the positive cone of an $L$ordered group and special type of elements of $L^G$ is found, where $G$ is a group.
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 arXiv:
 arXiv:1403.1542
 Bibcode:
 2014arXiv1403.1542B
 Keywords:

 Mathematics  Group Theory;
 06F15