Redox reactions as experimental examples of ternary weak algebraic hyperstructures
The authors point out that the algebraic structure of redox (oxidation-reduction) reactions of Ag, Cu, Am and Au can be described using weak associative ternary hyperoperations. A ternary hyperoperation on a set \(H\) is a mapping \(f:{H^3} \to {{\mathcal P}^*}(H)\). The operation is weak associative iff for \(\forall {a_1},{a_2},a_3^{},{a_4},{a_5} \in H\) \(f(f({a_1},{a_2},{a_3}),{a_4},{a_5}) \cap f({a_1},f({a_2},{a_3},{a_4}),{a_5}) \neq \emptyset \), \(f(f({a_1},{a_2},{a_3}),{a_4},{a_5}) \cap f({a_1},{a_2},f({a_3},{a_4},{a_5})) \neq \emptyset \) and \(f({a_1},f({a_2},{a_3},{a_4}),{a_5}) \cap f({a_1},{a_2},f({a_3},{a_4},{a_5})) \neq \emptyset \) holds.
scientific article; zbMATH DE number 6914256
scientific article