Semirings which are union of principal left k-radicals

Abstract

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 l ∞ of the relation −→l on a semiring S, given by for a, b ∈ S, a −→l b ⇔ bn ∈ Sa for some n ∈ N.