Locally Closed Semirings and Iteration Semirings |
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Authors: | Xianzhong Zhao |
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Institution: | (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: | 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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