Rationally Additive Semirings Zoltán Ésik Werner Kuich November 2001

### Abstract:

We define rationally additive semirings that are a generalization of ()complete and (-)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

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