Geodesic
On infinity of the free $3$-generated lattice with one left modular generator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 528-532 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the free lattice generated by three elements one of which is left modular. We prove that the lattice is infinite.
Keywords: free lattice, left modular element, right modular element. 
@article{SEMR_2017_14_a14,
     author = {M. P. Shushpanov},
     title = {On infinity of the free $3$-generated lattice with one left modular generator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {528--532},
     year = {2017},
     volume = {14},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a14/}
}
TY  - JOUR
AU  - M. P. Shushpanov
TI  - On infinity of the free $3$-generated lattice with one left modular generator
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 528
EP  - 532
VL  - 14
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a14/
LA  - ru
ID  - SEMR_2017_14_a14
ER  - 
%0 Journal Article
%A M. P. Shushpanov
%T On infinity of the free $3$-generated lattice with one left modular generator
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 528-532
%V 14
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a14/
%G ru
%F SEMR_2017_14_a14
M. P. Shushpanov. On infinity of the free $3$-generated lattice with one left modular generator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 528-532. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a14/

[1] G. Grätzer, Lattice Theory: Foundation, Springer Science Business Media, 2011 | MR

[2] M. Stern, Semimodular Lattices. Theory and Applications, Cambridge University Press, 1999 | MR | Zbl

[3] O. Ore, “On the theorem of Jordan–Holder”, Trans. Amer. Math. Soc., 41 (1937), 266–275 | MR

[4] S. P. Bhatta, “A characterization of neutral elements by the exclusion of sublattices”, Discrete Math., 309:6 (2009), 1691–1702 | DOI | MR | Zbl

[5] A. G. Gein, M. P. Shushpanov, “Finitely generated lattices with completely modular elements among generators”, Algebra and Logic, 52:6 (2014), 435–441 | DOI | MR | Zbl

[6] A. G. Gein, M. P. Shushpanov, “Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type”, Sibirian Mathematical Journal, 56:4 (2015), 631–636 | DOI | MR | Zbl

[7] S. P. Bhatta, “On the Problem of Characterizing Standard Elements by the Exclusion of Sublattices”, Order, 28 (2011), 565–576 | DOI | MR | Zbl