We show that the equatorial semiring Z(min) = (Z or { + infinity}, min
, + ) is a Fatou extension of the tropical semiring M = (N or { + infi
nity}, min, + ). This property allows us to give partial decidability
results for the equality problem for rational series with multipliciti
es in the tropical semiring. We also deduce from it the decidability o
f the limitedness problem for the equatorial semiring, solving therefo
re a question of 1. Simon.