Syntactic semigroup problem for the semigroup reducts of Affine Near-semirings over Brandt Semigroups

The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of $A^{+}(B_n)$, the affine near-semiring over a Brandt semigroup $B_n$. It is ascertained that both the semigroup reducts of $A^{+}(B_n)$ are syntactic semigroups.