On finite critical lattices. II
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 278-292

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Critical lattices are considered, i.e., lattices without nontrivial endomorphisms and not containing nontrivial proper sublattices without nontrivial endomorphisms. It is proved that there exist $n$-element critical lattices for $n=7$ and $n\geq9$.
Keywords: lattice, critical lattice.
Mots-clés : sublattice, endomorphism
O. E. Perminova. On finite critical lattices. II. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 278-292. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a25/
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[1] Vazhenin Yu. M., Perminov E. A., “O zhestkikh reshetkakh i grafakh”, Issled. po sovrem. algebre, mezhvuz. sb. st., Mat. zapiski, 2, no. 3, Sverdlovsk, 1979, 3–21 | MR

[2] Perminova O. E., “O konechnykh kriticheskikh reshetkakh”, Trudy Instituta matematiki i mekhaniki UrO RAN, 15, no. 2, 2009, 185–193

[3] Grettser G., Obschaya teoriya reshetok, Mir, M., 1982, 456 pp. | MR

[4] Rival I., “Lattices with doubly irreducible elements”, Can. Math. Bull., 17 (1974), 91–95 | DOI | MR | Zbl

[5] A. M. Kutin, A. V. Purgin, M. V. Kevbrin, V. V. Gulnov, “O dvukh zadachakh teorii reshetok”, Mezhdunar. algebraich. konf., posvyasch. pamyati D. K. Fadeeva, tez. dokl., S.-Peterburg, 1997, 231–232

[6] Perminova O. E., Diagrammy semielementnykh i vosmielementnykh reshetok, Kafedra algebry i diskretnoi matematiki UrFU [sait], (data obrascheniya 3.08.2011) URL: http://www.kadm.math.usu.ru/pages.php?id=perminova_papers