Borzooei, R., Hosseini, F., Zahiri, O. (2017). Convex $L$-lattice subgroups in $L$-ordered groups. Categories and General Algebraic Structures with Applications, (), -.

Rajabali Borzooei; Fateme Hosseini; Omid Zahiri. "Convex $L$-lattice subgroups in $L$-ordered groups". Categories and General Algebraic Structures with Applications, , , 2017, -.

Borzooei, R., Hosseini, F., Zahiri, O. (2017). 'Convex $L$-lattice subgroups in $L$-ordered groups', Categories and General Algebraic Structures with Applications, (), pp. -.

Borzooei, R., Hosseini, F., Zahiri, O. Convex $L$-lattice subgroups in $L$-ordered groups. Categories and General Algebraic Structures with Applications, 2017; (): -.

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

^{1}Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran.

^{2}University 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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