Brief communications

On finiteness of $3$-generated lattice with left modular and separating elements among generators

M. P. Shushpanov

Ural Federal University, 51 Lenina Ave., Ekaterinburg, 620000 Russia

Abstract: We prove that a $3$-generated lattice with modular and separating generators contains at most fourty seven elements. This estimate is stated to be sharp.

Keywords: lattice, left modular element, separating element, defining relation.

UDC: 512.565

Received: 24.10.2018
Revised: 24.10.2018
Accepted: 19.12.2018

DOI: 10.26907/0021-3446-2019-5-92-94

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:5, 82–84

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