Geodesic
On generalization of the notion of Moufang loop to n-ary case
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 52-70.

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

Using isotopical approach we generalize concept of binary Moufang loop on n-ary (n>2) case. We give two examples of ternary Moufang loop which are not a ternary group. 
@article{BASM_2019_1_a4,
     author = {V. I. Onoi and L. A. Ursu},
     title = {On generalization of the notion of {Moufang} loop to $n$-ary case},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {52--70},
     publisher = {mathdoc},
     number = {1},
     year = {2019},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2019_1_a4/}
}
TY  - JOUR
AU  - V. I. Onoi
AU  - L. A. Ursu
TI  - On generalization of the notion of Moufang loop to $n$-ary case
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2019
SP  - 52
EP  - 70
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2019_1_a4/
LA  - en
ID  - BASM_2019_1_a4
ER  - 
%0 Journal Article
%A V. I. Onoi
%A L. A. Ursu
%T On generalization of the notion of Moufang loop to $n$-ary case
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2019
%P 52-70
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2019_1_a4/
%G en
%F BASM_2019_1_a4
V. I. Onoi; L. A. Ursu. On generalization of the notion of Moufang loop to $n$-ary case. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 52-70. https://geodesic-test.mathdoc.fr/item/BASM_2019_1_a4/

[1] Belousov V. D., Foundations of the theory of quasigroups and loops, Nauka, M., 1967 (in Russian) | MR

[2] Belousov V. D., $n$-ary quasigroups, Ştiinţa, Chisinau, 1972 (in Russian) | MR

[3] Kurosh A. G., General algebra. Lectures during academic year 1969–1970, Nauka, M., 1974 (in Russian) | MR

[4] Kurosh A. G., Lectures on general algebra, Nauka, M., 1973 (in Russian) | MR | Zbl

[5] Bertram W., Kinyon M., “Torsors and ternary Moufang loops arising in projective geometry”, Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics Statistics, 85, eds. Makhlouf A., Paal E., Silvestrov S., Stolin A., Springer, Berlin–Heidelberg, 343–360 | DOI | MR | Zbl

[6] Bertram W., Kinyon M., Torsors and ternary Moufang loops arising in projective geometry, June 2012, arXiv: 1206.2222 | MR