Semidirect products in algebraic logic and solutions of the quantum Yang-Baxter equation

A semidirect product is introduced for cycloids, i. e. sets with a binary operation satisfying (x . y) . (x . z) = (y . x) . (y . z). Special classes of cycloids arise in the combinatorial theory of the quantum Yang-Baxter equation, and in algebraic logic. In the first instance, semidirect products can be used to construct new solutions of the quantum Yang - Baxter equation, while in algebraic logic, they lead to a characterization of L-algebras satisfying a general Glivenko type theorem.