Here we study the principal left k-radicals of a semiring with semilattice additive reduct and characterize the semirings which are disjoint union of principal left k-radicals via the transitive closure ... ∞ of the relation ... on a semiring S, given by for a, b ∈ S, a ... b ⇔ bn ∈ Sa for some n ∈ ℕ.