L-ordered and L-lattice ordered groups
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 special type of elements of LG L G is found, where G is a group.
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