Convex $L$-lattice subgroups in $L$-ordered groups | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 9، شماره 1، مهر 2018، صفحه 139-161 اصل مقاله (728.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.9.1.139 | ||
| نویسندگان | ||
| Rajabali Borzooei* 1؛ Fateme Hosseini1؛ Omid Zahiri2 | ||
| 1Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran. | ||
| 2University of Applied Science and Technology, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| $L$-ordered group؛ convex $L$-subgroup؛ (normal) convex $L$-lattice subgroup | ||
| مراجع | ||
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