Semiring identities in the semigroup $B_0$

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.