The form of multi-additive symmetric functions
The main result of this paper is the characterization of multi-additive symmetric functions for quite general structures like abelian groups and semigroups in the form of a composition of an additive function with the product of additive functions. It is also shown that every two \(n\)-additive functions, defined on a product of groups, with equal counterimages of the positive half-line must be proportional.
scientific article; zbMATH DE number 6965776
scientific article