2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98405General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built, connection with the standard theory is considered and several concrete examples are constructed. For clarity the shortened versions of classical Gluskin-Hosszú and Post theorems are given for them.18 pages, AmSLaTeXGroup TheoryHigh Energy Physics - TheoryMathematical PhysicsRings and AlgebrasRepresentation Theorytext