Finitely generated lattices with $M$-standard elements among generators

A. G. Gein

Chair of Algebra and Discrete Mathematics, Ural Federal University, 19 Mira str., Ekaterinburg, 620002 Russia

Abstract: We prove that a lattice is modular if it is generated by three elements, two of which are $M$-standard. We also show that a lattice generated by $n$, $n>3$, $M$-standard elements must not necessarily be modular.

Keywords: modular lattice, left-modular element, right-modular element, $M$-standard element.

UDC: 512.565

Received: 13.08.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:3, 14–17

Bibliographic databases:

• 
•