On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1215-1219
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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.
@article{SEMR_2017_14_a34,
author = {M. P. Shushpanov},
title = {On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {1215--1219},
year = {2017},
volume = {14},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a34/}
}
TY - JOUR AU - M. P. Shushpanov TI - On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements JO - Sibirskie èlektronnye matematičeskie izvestiâ PY - 2017 SP - 1215 EP - 1219 VL - 14 UR - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a34/ LA - en ID - SEMR_2017_14_a34 ER -
%0 Journal Article %A M. P. Shushpanov %T On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements %J Sibirskie èlektronnye matematičeskie izvestiâ %D 2017 %P 1215-1219 %V 14 %U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a34/ %G en %F SEMR_2017_14_a34
M. P. Shushpanov. On the embedding of the free lattice of rank $3$ in the lattice freely generated by three completely right modular elements. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1215-1219. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a34/
[1] Grätzer G., Lattice Theory: Foundation, Springer Science Business Media, 2011 | MR
[2] Stern M., Semimodular Lattices, Cambridge University Press, Cambridge, 1999 | MR | Zbl
[3] Bhatta S. P., “On the problem of characterizing standard elements by the exclusion of sublattices”, Order, 28:3 (2011), 565–576 | DOI | MR | Zbl
[4] Shushpanov M. P., “Lattices Generated by Modular Elements”, Russian Mathematics (Iz. VUZ), 59:12 (2015), 73–75 | MR | Zbl
[5] Gein A. G., Shushpanov M. P., “Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type”, Siberian Mathematical Journal, 56:4 (2015), 631–636 | DOI | MR | Zbl