Locally Closed Semirings |
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| Authors: | Z. ésik and W. Kuich |
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| Affiliation: | (1) Department of Applied Mathematics and Applied Physics, Xi’an Institute of Posts and Telecommunications, 710061 Xi’an, People’s Republic of China;(2) Department of Mathematics Education (and RINS), Gyeongsang National University, Jinju, 660-701, Republic of Korea |
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| 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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