*-Continuous Idempotent Left Semirings and Their Ideal Completion

Authors:
Hitoshi Furusawa;Fumiya Sanda
Affiliations:
Department of Mathematics and Computer Science, Kagoshima University,;Department of Mathematics and Computer Science, Kagoshima University,
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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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.