Binary operations and lattice structure for a model of matching with contracts

A binary operation-based representation of a lattice

“…Since their introduction, they have become the key notion in the definitions of groups, monoids, semigroups, rings, and in more algebraic structures studied in abstract algebra [5,16,18,26]. Binary operations have become essential tools in lattice theory and its applications, several notions and properties, and the notion of the lattice itself can be interpreted in terms of binary operations on it [7,10,11,20,24,25]. Furthermore, it is not surprising that binary operations with specific properties appear in various theoretical and application fields.…”