  We define Dedekind semidomains as semirings in which each nonzero fractional
ideal is invertible. Then we find some equivalent condition for semirings to
being Dedekind. For example, we prove that a Noetherian semidomain is Dedekind
if and only if it is multiplication. Then we show that a subtractive Noetherian
semidomain is Dedekind if and only if it is a $\pi$-semiring and each of it
nonzero prime ideal is invertible. We also show that the maximum number of the
generators of each ideal of a subtractive Dedekind semidomain is 2.
