  In the first section of this paper, we introduce the notions of fractional
and invertible ideals of semirings and characterize invertible ideals of a
semidomain. In section two, we define Pr\"{u}fer semirings and characterize
them in terms of valuation semirings. In this section, we also characterize
Pr\"{u}fer semirings in terms of some identities over its ideals such as $(I +
J)(I \cap J) = IJ$ for all ideals $I$, $J$ of $S$. In the third section, we
give a semiring version for the Gilmer-Tsang Theorem, which states that for a
suitable family of semirings, the concepts of Pr\"{u}fer and Gaussian semirings
are equivalent. At last we end this paper by giving a plenty of examples of
proper Gaussian and Pr\"{u}fer semirings.
