Abstract
Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. esik 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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