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Convex isomorphic ordered sets. (English) Zbl 0780.06001
Summary: V. I. Marmazeev introduced [Uporyad. Mnozhestva Reshetki 9, 50-58 (1986; Zbl 0711.06005)] 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 lattices are convex isomorphic, in particular for modular, distributive and complemented lattices.
The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered sets. These concepts were defined by I. Chajda [Arch. Math., Brno 28, No. 1-2, 25-34 (1992)], I. Chajda and J. Rachůnek [Order 5, 407-423 (1989; Zbl 0674.06003)] and J. Larmerová and J. Rachůnek [Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 91, Math. 27, 13-23 (1988; Zbl 0693.06003)].

06A06 Partial orders, general
06B15 Representation theory of lattices
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