Borzooei, R., Hosseini, F., Zahiri, O. (2018). Convex $L$-lattice subgroups in $L$-ordered groups. Categories and General Algebraic Structures with Applications, 9(1), 139-161.
Rajabali Borzooei; Fateme Hosseini; Omid Zahiri. "Convex $L$-lattice subgroups in $L$-ordered groups". Categories and General Algebraic Structures with Applications, 9, 1, 2018, 139-161.
Borzooei, R., Hosseini, F., Zahiri, O. (2018). 'Convex $L$-lattice subgroups in $L$-ordered groups', Categories and General Algebraic Structures with Applications, 9(1), pp. 139-161.
Borzooei, R., Hosseini, F., Zahiri, O. Convex $L$-lattice subgroups in $L$-ordered groups. Categories and General Algebraic Structures with Applications, 2018; 9(1): 139-161.
Convex $L$-lattice subgroups in $L$-ordered groups
1Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.
2University of Applied Science and Technology, Tehran, Iran
Abstract
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.
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