Multiplicative band semirings and distributive lattices

In this paper, we investigate multiplicative semirings with identity element. From the algebraic properties of lattices and distributive lattices, we study some properties of multiplicatice semirngs with identity. We show that if S, which is a semirings with identity, is a multiplicative band semiring if and only if S is a distributive lattice. Finally, we obtain a representation theorem for distributive lattices.