Galois relation for closed classes of discrete functions
Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 10-15.

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

Galois theory for $S$-closed classes of discrete functions is formulated. In particular cases, these classes coincide with the superposition-closed classes of functions of multivalued logics, with clones, with the hereditary systems of discrete functions and with the classes of functions computed by switching circuits.
Keywords: closed class, clone, discrete function.
Mots-clés : Galois connection
@article{PDM_2010_2_a1,
     author = {N. G. Parvatov},
     title = {Galois relation for closed classes of discrete functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {10--15},
     publisher = {mathdoc},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_2_a1/}
}
TY  - JOUR
AU  - N. G. Parvatov
TI  - Galois relation for closed classes of discrete functions
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2010
SP  - 10
EP  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2010_2_a1/
LA  - ru
ID  - PDM_2010_2_a1
ER  - 
%0 Journal Article
%A N. G. Parvatov
%T Galois relation for closed classes of discrete functions
%J Prikladnaâ diskretnaâ matematika
%D 2010
%P 10-15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2010_2_a1/
%G ru
%F PDM_2010_2_a1
N. G. Parvatov. Galois relation for closed classes of discrete functions. Prikladnaâ diskretnaâ matematika, no. 2 (2010), pp. 10-15. http://geodesic.mathdoc.fr/item/PDM_2010_2_a1/

[1] Kurosh A. G., Lektsii po obschei algebre, Izd-vo “Lan”, SPb., 2005

[2] Bodnarchuk V. G., Kaluzhnin L. A., Kotov V. N., Romov B. A., “Teoriya Galua dlya algebr Posta”, Kibernetika, 1969, no. 3, 1–10 ; no. 5, 1–9 | MR | Zbl

[3] Geiger D., “Closed systems of functions and predicates”, Pacific journal of mathematics, 27:1 (1968), 95–100 | MR | Zbl

[4] Pippenger N., “Galois theory for minors of finite functions”, Discrete Mathematics, 254 (2002), 405–419 | DOI | MR | Zbl

[5] Pöshel R., Kalužnin L. A., Funktionen- und Relationenalgebren, WEB Deutscher Verlag der Wissenschaften, Berlin, 1979 | MR

[6] Hellerstein L., “On generalized constraints and certificates”, Discrete Mathematics, 226 (2001), 211–232 | DOI | MR | Zbl

[7] Maltsev A. I., Iterativnye algebry Posta, Izd-vo Novosib. un-ta, Novosibirsk, 1976 | MR

[8] Maltsev A. I., “Iterativnye algebry i mnogoobraziya Posta”, Algebra i logika, 5:2 (1966), 5–24 | MR

[9] Parvatov N. G., “Nasledstvennye sistemy diskretnykh funktsii”, Diskret. analiz i issled. operatsii. Ser. 2, 14:2 (2007), 76–91 | MR