Geodesic
Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators
Algebra i logika, Tome 57 (2018) no. 3, pp. 362-376.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.
Keywords: left-modular element, right-modular element, seminormal element, defining relation. 
@article{AL_2018_57_3_a6,
     author = {M. P. Shushpanov},
     title = {Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators},
     journal = {Algebra i logika},
     pages = {362--376},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/}
}
TY  - JOUR
AU  - M. P. Shushpanov
TI  - Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators
JO  - Algebra i logika
PY  - 2018
SP  - 362
EP  - 376
VL  - 57
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/
LA  - ru
ID  - AL_2018_57_3_a6
ER  - 
%0 Journal Article
%A M. P. Shushpanov
%T Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators
%J Algebra i logika
%D 2018
%P 362-376
%V 57
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/
%G ru
%F AL_2018_57_3_a6
M. P. Shushpanov. Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators. Algebra i logika, Tome 57 (2018) no. 3, pp. 362-376. http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/

[1] G. Grettser, Obschaya teoriya reshetok, Mir, M., 1982

[2] P. R. Jones, “Distributive, modular and separating elements in lattices”, Rocky Mt. J. Math., 13:3 (1983), 429–436 | DOI | MR | Zbl

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

[4] G. Grätzer, E. T. Schmidt, “Standard ideals in lattices”, Acta Math. Acad. Sci. Hung., 12 (1961), 17–86 | DOI | MR | Zbl

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

[6] A. G. Gein, M. P. Shushpanov, “Dostatochnye usloviya modulyarnosti reshetki s porozhdayuschimi elementami, obladayuschimi svoistvami tipa modulyarnosti”, Sib. matem. zh., 56:4 (2015), 798–804 | MR | Zbl

[7] A. G. Gein, M. P. Shushpanov, “Modulyarnost i distributivnost 3-porozhdënnykh reshëtok so spetsialnymi elementami sredi porozhdayuschikh”, Algebra i logika, 56:1 (2017), 3–19 | DOI | MR | Zbl

[8] N. A. Minigulov, “On 3-generated lattices with standard and dual standard elements among generators”, Int. conf. and PhD-master summer school on graphs and groups, spectra and symmetries (Akademgorodok, Novosibirsk, Russia, 15–28 August 2016) http://math.nsc.ru/conference/g2/g2s2/exptext/Minigulov-abstract-G2S2

[9] A. G. Gein, M. P. Shushpanov, “Konechnoporozhdënnye reshëtki s vpolne modulyarnymi elementami sredi porozhdayuschikh”, Algebra i logika, 52:6 (2013), 657–666 | MR

[10] M. P. Shushpanov, “O konechnosti 3-porozhdennoi reshetki s ogranicheniyami tipa modulyarnosti na porozhdayuschie elementy”, Mezhd. konf. “Maltsevskie chteniya” (21–25 noyabrya 2016, Novosibirsk), Tez. dokl., IM SO RAN i NGU, Novosibirsk, 2016 http://www.math.nsc.ru/conference/malmeet/16/malmeet16.pdf