L-Ordered and L-Lattice Ordered Groups

2014/03/06 by R. A. Borzooei, Borzooei, R. A., Anatolij Dvurečenskij +3
Decision Sciences · Computer Science · Mathematics · #Fuzzy and Soft Set Theory #Advanced Algebra and Logic #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1403.1542

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.

Related

• Ordering groups and validity in lattice-ordered groups
• Proof Theory and Ordered Groups
• HNN extensions of quasi-lattice ordered groups and their operator algebras
• Orders on groups, and spectral spaces of lattice-groups
• Partially ordered semigroups and groups with two mixed partial orderings