Naslov
Cubic structure

Autori
Volenec, Vladimir ; Kolar-Begović, Zdenka ; Kolar- Šuper, Ružica

Izvornik
Glasnik matematički (0017-095X) 52 (2017), 2; 247-256

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
TSM-quasigroup, commutative group, ternary relation, cubic structure

Sažetak
In this paper we examine the relationships between cubic structures, totally symmetric medial quasigroups, and commutative groups. We prove that the existence of a cubic structure on the given set is equivalent to the existence of a totally symmetric medial quasigroup on this set, and it is equivalent to the existence of a commutative group on this set. We give also some interesting geometric examples of cubic structures. By means of these examples, each theorem that can be proved for an abstract cubic structure has a number of geometric consequences. In the final part of the paper, we prove also some simple properties of abstract cubic structures.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA