A. G. Gein, M. P. Shushpanov, “Modularity and distributivity of <nobr>$3$</nobr>-generated lattices with special elements among generators”, Algebra Logika, 2017, Volume 56, Number 1,Pages <nobr>3

This article is cited in 4 papers

Modularity and distributivity of $3$-generated lattices with special elements among generators

A. G. Gein, M. P. Shushpanov

El'tsyn Ural Federal University, ul. Mira 19, Yekaterinburg, 620002, Russia

Abstract: 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.

Keywords: modular lattice, distributive lattice, left modular element, right modular element, distributive element, standard element.

UDC: 512.565

Received: 08.07.2015
Revised: 17.11.2015

DOI: 10.17377/alglog.2017.56.101