In this note we introduce the concept of strongly prime one-sided ideal in semirings. It is shown that in a semiring every maximal right ideal is strongly prime and every strongly prime right ideal is prime. We characterize strongly prime right ideals in a semiring interms of /r-systems. It is observed that if an ideal / in a semiring R is strongly prime as a right ideal if and only if / is completely prime. We further prove that if Ψ is a homomorphism of a yoked semiring Ronto a plain semiring S, then there is a one-to-one correspondence between the set of all subtractive strongly prime right ideals of R containing Ker(Ψ) and the set of all subtractive strongly prime right ideals of S.
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