  The semigroup $B_0$ is the only, up to isomorphism, 4-element subsemigroup of
the 5-element Brandt semigroup $B_2$. Being an inverse semigroup, the semigroup
$B_2$ can naturally be considered an additively idempotent semiring and $B_0$
is its subsemiring. We show that the semiring $B_0$ has a finite basis of
identities.
