L-ordered and L-lattice ordered groups

@article{Borzooei2015LorderedAL,
  title={L-ordered and L-lattice ordered groups},
  author={Rajab Ali Borzooei and Anatolij Dvurecenskij and Omid Zahiri},
  journal={Inf. Sci.},
  year={2015},
  volume={314},
  pages={118-134}
}
This paper pursues an investigation on groups equipped with an L-ordered relation, where L is a fixed complete Heyting algebra. First, by the concept of join and meet on an L-ordered set, the notion of an L-lattice (a weak 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… Expand
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