Modularity and Distributivity of 3-Generated Lattices with Special Elements Among Generators

We consider 3-generated lattices whose generating elements possess properties that are, in a sense, close to modularity or distributivity. Those combinations of these properties are specified that are sufficient for a lattice to be modular, and even distributive.

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Bibliographic Details
Published in:Algebra and logic 2017-03, Vol.56 (1), p.1-12
Main Authors: Gein, A. G., Shushpanov, M. P.
Format: Article
Language:English
Subjects:
Algebra
Lattice theory
Lattices (mathematics)
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Modularity
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Description
Summary:We consider 3-generated lattices whose generating elements possess properties that are, in a sense, close to modularity or distributivity. Those combinations of these properties are specified that are sufficient for a lattice to be modular, and even distributive.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-017-9423-z