Lattices with Defining Relations Close to Distributivity

We consider the 3-generated lattices whose generators enjoy the defining relations of the type a ∨( b ∧ c ) = ( a ∨ b )∧( a ∨ c ). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.

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Bibliographic Details
Published in:Siberian mathematical journal 2017-11, Vol.58 (6), p.983-989
Main Authors: Gein, A. G., Shushpanov, M. P.
Format: Article
Language:English
Subjects:
Lattices
Mathematics
Mathematics and Statistics
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Description
Summary:We consider the 3-generated lattices whose generators enjoy the defining relations of the type a ∨( b ∧ c ) = ( a ∨ b )∧( a ∨ c ). Moreover, if the lattice is finite then we obtain its diagram; otherwise, we prove that the corresponding lattice is infinite.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446617060076