Rationally Additive Semirings

Abstract

We define rationally additive semirings that are a generalization of (omega-)complete and (omega-)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 N_infty, the semiring of natural numbers equipped with a top element, as the free rationally additive semirings.