Locally Closed Semirings and Iteration Semirings |
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Authors: | Xianzhong Zhao |
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Institution: | (1) Northwest University, Xian, Shaanxi, P.R. China |
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Abstract: | Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring. |
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Keywords: | 2000 Mathematics Subject Classifications: 16Y60 68Q70 20M07 |
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