Rationally Additive Semirings

  • Zoltán Ésik
  • Werner Kuich


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.
How to Cite
Ésik, Z., & Kuich, W. (2001). Rationally Additive Semirings. BRICS Report Series, 8(42). https://doi.org/10.7146/brics.v8i42.21702