Geodesic
Clone classification of dually discriminator algebras with finite support
Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 359-366.

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

Dually discriminator algebras are considered up to clones generated by the algebra operations. In terms of binary relations, all clones of the operators on a finite set that contain the Pixley dual discriminator are efficiently described. As a consequence, a similar clone classification of quasi-primal algebras with finite support is determined. 
@article{MZM_1997_61_3_a4,
     author = {S. S. Marchenkov},
     title = {Clone classification of dually discriminator algebras with finite support},
     journal = {Matemati\v{c}eskie zametki},
     pages = {359--366},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a4/}
}
TY  - JOUR
AU  - S. S. Marchenkov
TI  - Clone classification of dually discriminator algebras with finite support
JO  - Matematičeskie zametki
PY  - 1997
SP  - 359
EP  - 366
VL  - 61
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a4/
LA  - ru
ID  - MZM_1997_61_3_a4
ER  - 
%0 Journal Article
%A S. S. Marchenkov
%T Clone classification of dually discriminator algebras with finite support
%J Matematičeskie zametki
%D 1997
%P 359-366
%V 61
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a4/
%G ru
%F MZM_1997_61_3_a4
S. S. Marchenkov. Clone classification of dually discriminator algebras with finite support. Matematičeskie zametki, Tome 61 (1997) no. 3, pp. 359-366. http://geodesic.mathdoc.fr/item/MZM_1997_61_3_a4/

[1] Fried E., Pixley A. F., “The dual discriminator function in universal algebra”, Acta Sci. Math., 41:1–2 (1979), 83–100 | MR | Zbl

[2] Csákány B., Gavalcová T., “Finite homogeneous algebras, I”, Acta Sci. Math., 42:1–2 (1980), 57–65 | MR | Zbl

[3] Grätzer G., Universal algebra, Van Nostrand, Princeton, 1968 | Zbl

[4] Baker K. A., Pixley A. F., “Polynomial interpolation and the Chinese remainder theorem for algebraic systems”, Math. Z., 143 (1975), 165–174 | DOI | MR | Zbl

[5] Marchenkov S. S., “O zamknutykh klassakh samodvoistvennykh funktsii mnogoznachnoi logiki”, Problemy kibernetiki, 1979, no. 36, 5–22 | MR | Zbl

[6] Marchenkov S. S., “Ob odnorodnykh algebrakh”, Dokl. AN SSSR, 256:4 (1981), 787–790 | MR | Zbl

[7] Marchenkov S. S., “Odnorodnye algebry”, Problemy kibernetiki, 1982, no. 39, 85–106 | MR | Zbl

[8] Marchenkov S. S., “O klassifikatsii algebr so znakoperemennoi gruppoi avtomorfizmov”, Dokl. AN SSSR, 265:3 (1982), 533–536 | MR | Zbl

[9] Marchenkov S. S., “Klassifikatsiya algebr so znakoperemennoi gruppoi avtomorfizmov”, Matem. voprosy kibernetiki, 1989, no. 2, 100–122 | MR | Zbl

[10] Marczewski E., “Homogeneous algebras and homogeneous operations”, Fund. Math., 56 (1964), 81–103 | MR | Zbl

[11] Pixley A. F., “The ternary discriminator function in universal algebra”, Math. Ann., 191 (1971), 167–180 | DOI | MR | Zbl

[12] Bondarchuk V. G., Kaluzhin L. A., Kotov V. N., Romov B. A., “Teoriya Galua dlya algebr Posta. I; II”, Kibernetika, 1969, no. 3, 1–10

[13] Post E. L., “Introduction to a general theory of elementary propositions”, Amer. J. Math., 43 (1921), 163–185 | DOI | MR

[14] Post E. L., Two-valued iterative systems of mathematical logic, Ann. of Math. Stud., 5, Univ. Press, Princeton, 1941 | MR | Zbl

[15] Yablonskii S. V., Gavrilov G. P., Kudryavtsev V. B., Funktsii algebry logiki i klassy Posta, Nauka, M., 1966 | Zbl

[16] Marchenkov S. S., Ugolnikov A. B., Zamknutye klassy bulevykh funktsii, Preprint, IPM AN SSSR, M., 1990

[17] Csákány B., Gavalcová T., “Three-element quasi-primal algebras”, Studia Sci. Math. Hungar., 16 (1981), 167–180 | MR

[18] Taimanov V. A., “O funktsionalnykh sistemakh $k$-znachnoi logiki s operatsiyami zamykaniya programmnogo tipa”, Dokl. AN SSSR, 268:6 (1983), 1307–1310 | MR | Zbl

[19] Solovev V. D., “Zamknutye klassy v $k$-znachnoi logike s operatsiei razvetvleniya po predikatu”, Diskretnaya matematika, 2:4 (1990), 19–25 | MR