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- W2762178303 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." @default.
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- W2762178303 date "2018-07-01" @default.
- W2762178303 modified "2023-09-27" @default.
- W2762178303 title "Convex $L$-lattice subgroups in $L$-ordered groups" @default.
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- W2762178303 doi "https://doi.org/10.29252/cgasa.9.1.139" @default.
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