Affine Near-Semirings over Brandt Semigroups

In order to study the structure of $A^{+}(B_n)$ – the affine near-semiring over a Brandt semigroup – this work completely characterizes the Green’s classes of its semigroup reducts. In this connection, this work characterizes the elements of $A^{+}(B_n)$ and reports the size of $A^{+}(B_n)$. Further, idempotents and regular elements of the semigroup reducts of $A^{+}(B_n)$ have also been characterized and studied some relevant semigroups in $A^{+}(B_n)$.