Representation of Steinitz's lattice in lattices of substructures of relational structures
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Date
2016
Authors
Bezushchak, Oksana
Oliynyk, Bogdana
Sushchansky, Vitaliy
Journal Title
Journal ISSN
Volume Title
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Abstract
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.
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Keywords
relational structure, lattice, supernatural numbers, Boolean algebra
Citation
Bezushchak Oksana. Representation of Steinitz's lattice in lattices of substructures of relational structures / Oksana Bezushchak, Bogdana Oliynyk, Vitaliy Sushchansky // Algebra and Discrete Mathematics. - 2016. - Vol 21, No 2. - P. 184-201.