TY - JOUR ID - 50748 TI - Convex $L$-lattice subgroups in $L$-ordered groups JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Borzooei, Rajabali AU - Hosseini, Fateme AU - Zahiri, Omid AD - Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran. AD - University of Applied Science and Technology, Tehran, Iran Y1 - 2018 PY - 2018 VL - 9 IS - 1 SP - 139 EP - 161 KW - $L$-ordered group KW - convex $L$-subgroup KW - (normal) convex $L$-lattice subgroup DO - 10.29252/cgasa.9.1.139 N2 - 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. UR - https://cgasa.sbu.ac.ir/article_50748.html L1 - https://cgasa.sbu.ac.ir/article_50748_0ee3783313053dea8791d1990de4c8e2.pdf ER -