Anatolii Zhuchok (Luhansk Taras Shevchenko National University, Poltava, Ukraine)
A trioid is an algebraic system consisting of a set with three binary associative operations satisfying certain axioms. Trioids are a generalization of semigroups. They play a prominent role in trialgebra theory. After defining the concept of a trioid we present examples of trioids and their relationships with such algebraic structures as Poisson algebras, Leibniz algebras, dialgebras, dimonoids, digroups and n-tuple semigroups. Then we establish independence of axioms of trioids and construct absolutely and relatively free algebras in trioid variety.
