This article is cited in 7 papers

Finitely generated lattices with completely modular elements among generators

A. G. Gein, M. P. Shushpanov

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

Abstract: 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.

Keywords: modular lattices, free lattices, modular elements.

UDC: 512.565

Received: 17.08.2013
Revised: 28.11.2013

 English version: Algebra and Logic, 2014, 52:6, 435–441

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