Geodesic
3-Generated lattices close to distributive ones
Algebra i logika, Tome 62 (2023) no. 4, pp. 504-523
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Lattices are considered in which, instead of distributive identities, a ‘gap’ of length at most 1 is allowed between the right and left parts of each distributivity relation. Such lattices are said to be close to distributive ones. Although this property is weaker than distributivity, nevertheless a 3-generated lattice with this property is also finite.
Keywords: weakened condition for distributivity, 3-generated lattice, finiteness of nonmodular lattice. 
@article{AL_2023_62_4_a3,
     author = {A. G. Gein and I. D. Maslintsyn and K. E. Maslintsyna and K. V. Selivanov},
     title = {3-Generated lattices close to distributive ones},
     journal = {Algebra i logika},
     pages = {504--523},
     year = {2023},
     volume = {62},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_4_a3/}
}
TY  - JOUR
AU  - A. G. Gein
AU  - I. D. Maslintsyn
AU  - K. E. Maslintsyna
AU  - K. V. Selivanov
TI  - 3-Generated lattices close to distributive ones
JO  - Algebra i logika
PY  - 2023
SP  - 504
EP  - 523
VL  - 62
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/AL_2023_62_4_a3/
LA  - ru
ID  - AL_2023_62_4_a3
ER  - 
%0 Journal Article
%A A. G. Gein
%A I. D. Maslintsyn
%A K. E. Maslintsyna
%A K. V. Selivanov
%T 3-Generated lattices close to distributive ones
%J Algebra i logika
%D 2023
%P 504-523
%V 62
%N 4
%U http://geodesic.mathdoc.fr/item/AL_2023_62_4_a3/
%G ru
%F AL_2023_62_4_a3
A. G. Gein; I. D. Maslintsyn; K. E. Maslintsyna; K. V. Selivanov. 3-Generated lattices close to distributive ones. Algebra i logika, Tome 62 (2023) no. 4, pp. 504-523. http://geodesic.mathdoc.fr/item/AL_2023_62_4_a3/

[1] G. Birkgof, Teoriya reshetok, Nauka, M., 1984

[2] 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

[3] M. P. Shushpanov, “Reshetki, porozhdennye modulyarnymi elementami”, Izv. vuzov. Matem., 2015, no. 12, 84–86 | MR | Zbl

[4] A. G. Gein, M. P. Shushpanov, “Sufficient conditions for the finiteness of the 3-generated lattice with modular and distributive type elements among generators”, Algebra Univers, 82:1 (2021), 8, 15 pp. | DOI | MR | Zbl

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

[6] R. A. Dean, “Component subsets of the free lattice on n generators”, Proc. Am. Math. Soc., 7 (1956), 220–226 | MR | Zbl

[7] A. G. Gein, I. D. Maslintsyn, K. E. Raboi, “O reshetkakh, blizkikh k distributivnym”, Mezhd. konf. "‘Maltsevskie chteniya"’, Tez. dokl. (19–23 avgusta 2019, Novosibirsk), IM SO RAN i NGU, Novosibirsk, 2019, 186 http://math.nsc.ru/conference/malmeet/19/maltsev19.pdf

[8] A. G. Gein, I. D. Maslintsyn, K. E. Raboi, “Opredelyayuschie sootnosheniya v 3-porozhdennoi reshetke, blizkoi k distributivnoi”, Mezhd. konf. "‘Maltsevskie chteniya"’, Tez. dokl. (16–20 noyabrya 2020, Novosibirsk), IM SO RAN i NGU, Novosibirsk, 2020, 220 http://math.nsc.ru/conference/malmeet/20/maltsev20.pdf

[9] A. G. Gein, I. D. Maslintsyn, K. E. Raboi, K. V. Selivanov, “Konechnost 3-porozhdennoi reshetki, blizkoi k distributivnoi”, Mezhd. konf. "‘Maltsevskie chteniya"’, Tez. dokl. (20–24 sentyabrya 2021, Novosibirsk), IM SO RAN i NGU, Novosibirsk, 2021, 149 http://math.nsc.ru/conference/malmeet/21/maltsev21.pdf