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Rationally Additive Semirings
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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.
Title: Rationally Additive Semirings
Description:
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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