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∗-Continuous Idempotent Left Semirings and Their Ideal Completion

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Relations and Kleene Algebra in Computer Science (RelMiCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5827))

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Abstract

In this paper, we introduce two notions of continuity for idempotent left semirings, which are called ∗-continuity and D-continuity. Also, for a ∗-continuous idempotent left semiring, we introduce a notion of ∗-ideals. Then, we show that the set of ∗-ideals of a ∗-continuous idempotent left semiring forms a D-continuous idempotent left semiring and the construction satisfies a universal property.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Kagoshima University,  

    Hitoshi Furusawa & Fumiya Sanda

Authors
  1. Hitoshi Furusawa
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  2. Fumiya Sanda
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität zu Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  2. College of Engineering, Qatar University, P.O. Box 2713, CSE 209, Doha, Qatar,  

    Ali Mohamed Jaoua

  3. Institut für Informatik, Universität Augsburg, Universitätsstr. 6a, 86135, Augsburg, Germany

    Bernhard Möller

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Furusawa, H., Sanda, F. (2009). ∗-Continuous Idempotent Left Semirings and Their Ideal Completion. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2009. Lecture Notes in Computer Science, vol 5827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04639-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-04639-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04638-4

  • Online ISBN: 978-3-642-04639-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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