Geodesic
Convex isomorphism of $Q$-lattices
Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 37-42

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MR Zbl
V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$-lattices defined in [2] and to characterize the convex isomorphic $q$-lattices.
V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$-lattices defined in [2] and to characterize the convex isomorphic $q$-lattices.
DOI : 10.21136/MB.1993.126019
Classification : 06A06, 06A10, 06B15
Keywords: quasiorder; convex isomorphism; $q$-lattices 
Emanovský, Petr. Convex isomorphism of $Q$-lattices. Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 37-42. doi: 10.21136/MB.1993.126019
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[1] Emanovský P.: Convex isomorphic ordered sets. Mathematica Bohemica 118 (1993), 29-35. | MR

[2] Chajda I.: Lattices in quasiordered set. Acta Univ. Palack. Olomouc 31 (1992), to appear. | MR

[3] Marmazejev V. I.: The lattice of convex sublattices of a lattice. Mežvuzovskij naučnyj sbornik, Saratov (1986), 50-58. (In Russian.) | MR

[4] Szász G.: Théorie des trellis. Akadémiai Kiadó, Budapest, 1971,

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