### Abstract

A Conway semiring is a semiring S equipped with a unary operation*: S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or N^{rat}≪Σ≫ of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conway identities. We introduce here partial Conway semirings, which are semirings S which have a star operation defined only on an ideal of S; when the arguments are appropriate, the operation satisfies the above identities. We develop the general theory of partial Conway semirings and prove a Kleene theorem for this generalization.

Original language | English |
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Pages (from-to) | 19-40 |

Number of pages | 22 |

Journal | Fundamenta Informaticae |

Volume | 86 |

Issue number | 1-2 |

Publication status | Published - Nov 17 2008 |

### Keywords

- Conway semiring
- Iteration semiring
- Kleene theorem

### ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

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## Cite this

*Fundamenta Informaticae*,

*86*(1-2), 19-40.