*-Continuous Kleene ω-Algebras

@article{sik2015ContinuousK,
  title={*-Continuous Kleene $\omega$-Algebras},
  author={Zolt{\'a}n {\'E}sik and Ulrich Fahrenberg and Axel Legay},
  journal={ArXiv},
  year={2015},
  volume={abs/1501.01118}
}
We define and study basic properties of \(^*\)-continuous Kleene \(\omega \)-algebras that involve a \(^*\)-continuous Kleene algebra with a \(^*\)-continuous action on a semimodule and an infinite product operation that is also \(^*\)-continuous. We show that \(^*\)-continuous Kleene \(\omega \)-algebras give rise to iteration semiring-semimodule pairs, and that for Buchi automata over \(^*\)-continuous Kleene \(\omega \)-algebras, one can compute the associated infinitary power series. 

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