Rationally Additive Semirings

Zoltán Ésik
Werner Kuich

November 2001


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

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