The Form of Multi-additive Symmetric Functions
Rafał Kucharski, Radosław Łukasik · Results in Mathematics · 2018
In this paper we show that every n -additive symmetric function, between quite general structures like abelian groups and semigroups, can be factorized into a composition of additive function with the product of additive functions. We also show that every two n -additive functions, defined on a product of groups, with equal counterimages of the positive half-line must be proportional.