Solution of Belousov's problem
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 93-103.

Voir la notice de l'article provenant de la source Library of Science

The authors prove that a local n-quasigroup defined by the equation
Keywords: n-ary quasigroup, reducible, irreducible
@article{DMGAA_2001_21_1_a8,
     author = {Akivis, Maks and Goldberg, Vladislav},
     title = {Solution of {Belousov's} problem},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {93--103},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a8/}
}
TY  - JOUR
AU  - Akivis, Maks
AU  - Goldberg, Vladislav
TI  - Solution of Belousov's problem
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2001
SP  - 93
EP  - 103
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a8/
LA  - en
ID  - DMGAA_2001_21_1_a8
ER  - 
%0 Journal Article
%A Akivis, Maks
%A Goldberg, Vladislav
%T Solution of Belousov's problem
%J Discussiones Mathematicae. General Algebra and Applications
%D 2001
%P 93-103
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a8/
%G en
%F DMGAA_2001_21_1_a8
Akivis, Maks; Goldberg, Vladislav. Solution of Belousov's problem. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 93-103. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a8/

[1] V.D. Belousov, n-ary quasigroups (Russian), Izdat. 'Shtiintsa', Kishinev 1972, 227 pp.

[2] V.D. Belousov, and M. D. Sandik, n-ary quasigroups and loops (Russian), Sibirsk. Mat. Zh. 7 (1966), no. 1, 31-54. (English transl. in: Siberian Math. J. 7 (1966), no. 1, 24-42).

[3] W. Blaschke, Einführung in die Geometrie der Waben, Birkhäuser-Verlag, Basel-Stuttgart 1955, 108 pp. (Russian transl. GITTL, Moscow 1959), 144 pp.

[4] V.V. Borisenko, Irreducible n-quasigroups on finite sets of composite order (Russian), Mat. Issled., Vyp. 51 (1979), 38-42.

[5] B.R. Frenkin, Reducibility and uniform reducibility in certain classes of n-groupoids II (Russian), Mat. Issled., Vyp. 7 (1972), no. 1 (23), 150-162.

[6] M.M. Glukhov, Varieties of (i, j)-reducible n-quasigroups (Russian), Mat. Issled., Vyp. 39 (1976), 67-72.

[7] M.M. Glukhov, On the question of reducibility of principal parastrophies of n-quasigroups (Russian), Mat. Issled., Vyp. 113 (1990), 37-41.

[8] V.V. Goldberg, The invariant characterization of certain closure conditions in ternary quasigroups (Russian), Sibirsk. Mat. Zh. 16 (1975), no. 1, 29-43. (English transl. in: Siberian Math. J. 16 (1975), no. 1, 23-34).

[9] V.V. Goldberg, Reducible (n+1)-webs, group (n+1)-webs, and (2n+2)-hedral (n+1)-webs of multidimensional surfaces (Russian), Sibirsk. Mat. Zh. 17 (1976), no. 1, 44-57. (English transl. in: Siberian Math. J. 17 (1976), no. 1, 34-44).

[10] V.V. Goldberg, Theory of Multicodimensional (n+1)-Webs, Kluwer Academic Publishers, Dordrecht, 1988, xxii+466 pp.

[11] E. Goursat, Sur les équations du second ordre a n variables, analogues a l'équation de Monge-Ampere, Bull. Soc. Math. France 27 (1899), 1-34.

[12] V.V. Ryzhkov, Conjugate nets on multidimensional surfaces (Russian), Trudy Moscow. Mat. Obshch. 7 (1958).