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Keywords:
quasiorder; convex isomorphism; $q$-lattices
quasiorder; convex isomorphism; $q$-lattices
Summary:
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.
References:
[1] Emanovský P.: Convex isomorphic ordered sets. Mathematica Bohemica 118 (1993), 29-35. MR 1213830
[2] Chajda I.: Lattices in quasiordered set. Acta Univ. Palack. Olomouc 31 (1992), to appear. MR 1212600
[3] Marmazejev V. I.: The lattice of convex sublattices of a lattice. Mežvuzovskij naučnyj sbornik, Saratov (1986), 50-58. (In Russian.) MR 0957970
[4] Szász G.: Théorie des trellis. Akadémiai Kiadó, Budapest, 1971,
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