Finitely Generated Lattices with Completely Modular Elements among Generators

We look at the concept of a completely modular element of a lattice, which is the modular analog of the well-known concept of a neutral element of a lattice. It is proved that a lattice is modular if it is generated by three elements of which two are completely modular. Also it is shown that a latti...

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Bibliographic Details
Published in:Algebra and logic 2014, Vol.52 (6), p.435-441
Main Authors: Gein, A. G., Shushpanov, M. P.
Format: Article
Language:English
Subjects:
Algebra
Fuzzy sets
Lattice theory
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
Set theory
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Summary:We look at the concept of a completely modular element of a lattice, which is the modular analog of the well-known concept of a neutral element of a lattice. It is proved that a lattice is modular if it is generated by three elements of which two are completely modular. Also it is shown that a lattice generated by n , n  > 3, completely modular elements must not necessarily be modular.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-014-9258-9