Ideal Theory in Commutative Semirings

In this paper, we analyze some results on ideal theory of commutative semirings with non-zero identity analogues to commutative rings with non-zero identity. Here we will make an intensive examination of the notions of Noetherian semirings, Artinian semirings, local semirings and strongly irreducible ideals in commutative semirings. It is shown that this notion inherits most of essential properties of strongly irreducible ideals of a commutative rings with non-zero identity. Also, the relationship among the families of primary ideals, irreducible ideals and strongly irreducible ideals of a semiring $R$ is considered.