Representation of Steinitz's lattice in lattices of substructures of relational structures
Оксана Безущак, Bogdana Oliynyk, Vitaliy Sushchansky · Electronic Kyiv-Mohyla Academy Institutional Repository (National University of Kyiv-Mohyla Academy) · 2016
General conditions under which certain relational structure contains a lattice of substructures isomorphic to Steinitz's lattice are formulated. Under some natural restrictions we consider relational structures with the lattice containing a sublattice isomorphic to the lattice of positive integers with respect to divisibility. We apply to this sublattice a construction that could be called ``lattice completion''. This construction can be used for different types of relational structures, in particular for universal algebras, graphs, metric spaces etc. Some examples are considered.