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 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...

Full description

Saved in:
Bibliographic Details
Main Authors Borzooei, R. A, Dvurečenskij, A, Zahiri, O
Format Journal Article
LanguageEnglish
Published 06.03.2014
Subjects
Mathematics - Group Theory
Online AccessGet full text

Cover

More Information
Summary: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.
DOI:10.48550/arxiv.1403.1542