The Cauchy equation on \(l\)-semigroups
A binary operation \(\oplus: [0,M]^2 \to[0,M]\) is called a pseudo-addition if the following properties are satisfied: commutativity, associativity, 0 is the neutral element, monotonicity i.e. \(x\leq x'\), \(y\leq y' \Rightarrow x\oplus y\leq x'\oplus y'\) and continuity i.e. \(x_n\to x\), \(y_n\to y \Rightarrow x_n\oplus y_n\to x\oplus y\). the pair \(([0,M], \oplus)\) is an \(l\)-semigroup. The authors give the general solution of the Cauchy equation on a general \(l\)-semigroup. Then they present some examples of solutions.
scientific article; zbMATH DE number 1761055