  The resultant plays a crucial role in (computational) algebra and algebraic
geometry. One of the most important and well known properties of the resultant
is that it is equal to the determinant of the Sylvester matrix. In 2008,
Odagiri proved that a similar property holds over the tropical semiring if one
replaces subtraction with addition. The tropical semiring belongs to a large
family of algebraic structures called commutative idempotent semiring. In this
paper, we prove that the same property (with subtraction replaced with
addition) holds over an \emph{arbitrary\/} commutative idempotent semiring.
