Rationally Additive Semirings

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 N, the semiring of natural numbers equipped with a top element, as the free rationally additive semirings. Key Words: semiring, complete semiring, iteration semiring, fixed point, power series. Category: F.4.3

• Type: Journal
• Year: 2002
• Where: JUCS
• Authors: Zoltán Ésik, Werner Kuich
• Keywords: Iteration, JUCS 2002, Rational Power Series, Semiring