Convex $L$-lattice subgroups in $L$-ordered groups

• Published in: Categories and general algebraic structures with applications Vol. 9; no. 1; pp. 139 - 161
• Main Authors: Borzooei, Rajabali, Hosseini, Fateme, Zahiri, Omid
• Format: Journal Article
• Language: English
• Published: Shahid Beheshti University 01.07.2018
• Subjects: (normal) convex $L$-lattice subgroup; convex $L$-subgroup; L$-ordered group
• ISSN: 2345-5853; 2345-5861
• DOI: 10.29252/CGASA.9.1.139

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result about the set of all convex subgroups of a lattice ordered group and prove that $C(G)$, the set of all convex $L$-lattice subgroups of an $L$-ordered group $G$, is an $L$-complete lattice on height one. Then we use these objects to construct the quotient $L$-ordered groups and state some related results.