Archimedian operations and copulas with applications to branching processes with interaction of particles

We consider generalized summation operations (commutative and associative binary operations) which are isomorphic to the addition. We establish the correspondence between operations and strictly Archimedean copulas and their properties. We investigate the possibility of application to branching processes with competition-like interaction of particles. We discuss the "Archimedity" concept applied to operations and copulas, as well as its possible extension to stochastic operations.