This article is cited in 2 papers

Finiteness and infiniteness of $3$-generated lattices with distributive elements among generators

M. P. Shushpanov

Ural Federal University, Ekaterinburg, Russia

Abstract: We consider $3$-generated lattices whose generators are distributive, dually distributive, right modular, dually right modular elements, or elements possessing a combination of these properties. For these lattices, we find all triples of generators that suffice for the generated lattice to be finite.

Keywords: distributive element, right modular element, finite lattice, infinite lattice.

UDC: 512.565

Received: 20.08.2018
Revised: 03.10.2018
Accepted: 17.10.2018

DOI: 10.33048/smzh.2019.60.419

 English version: Siberian Mathematical Journal, 2019, 60:4, 734–740

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