Open AccessRationally Additive Semirings
Author(s) -
Zoltán Ésik,
Werner Kuich
Publication year - 2001
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v8i42.21702
Subject(s) - semiring , mathematics , generalization , power series , omega , kleene algebra , formal power series , series (stratigraphy) , discrete mathematics , combinatorics , algebra over a field , pure mathematics , mathematical analysis , paleontology , physics , quantum mechanics , biology
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.