Rationally Additive Semirings

We define rationally additive semirings that are a generalization of (ω)-complete and (ω)-continuous semirings. We prove that every rationally additive semiring is an iteration semiring. Moreover, we characterize the semirings of rational power series with coefficients in , the semiring of natural numbers equipped with a top element, as the free rationally additive semirings 1.) C. S. Calude, K. Salomaa, S. Yu (eds.). Advances and Trends in Automata and Formal Languages. A Collection of Papers in Honour of the 60th Birthday of Helmut Jürgensen