This article is cited in 2 papers

Mathematical logic, algebra and number theory

On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements

M. P. Shushpanov

Ural Federal University, 19, Mira str, 620002, Ekaterinburg, Russia

Abstract: We consider the lattice freely generated by three elements, which are right modular and dually right modular simultaneously. We prove that this lattice contains the free lattice of rank $3$ as a sublattice.

Keywords: right modular element, dually right modular element, completely right modular element, free lattice.

UDC: 512.56

MSC: 06B25

Received October 1, 2017, published November 27, 2017

Language: English

DOI: 10.17377/semi.2017.14.103