This article is cited in 2 papers

Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators

M. P. Shushpanov

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

Abstract: It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.

Keywords: left-modular element, right-modular element, seminormal element, defining relation.

UDC: 512.565

Received: 25.11.2016
Revised: 23.02.2017

DOI: 10.17377/alglog.2018.57.307

 English version: Algebra and Logic, 2018, 57:3, 237–247

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