Abstract.
We call a semiring S locally closed if for all a ∈ S there is some integer k such that 1 + a + ⋯ + a k =1 + a + ⋯ + a k + 1. In any locally closed semiring we may define a star operation a ↦ a *, where a * is the above finite sum. We prove that when S is locally closed and commutative, then S is an iteration semiring.
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Partially supported by grant no. T30511 from the National Foundation of Hungary for Scientific Research and the Austrian–Hungarian Bilateral Research and Development Fund, no. A-4/1999, and by the Austrian–Hungarian Action Foundation.
Partially supported by the Austrian–Hungarian Bilateral Research and Development Fund, no. A-4/1999, and by the Austrian–Hungarian Action Foundation.
Received March 16, 2001
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Ésik, Z., Kuich, W. Locally Closed Semirings. Monatsh. Math. 137, 21–29 (2002). https://doi.org/10.1007/s00605-001-0481-9
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DOI: https://doi.org/10.1007/s00605-001-0481-9