A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x ∈ S such that a + axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e ∈ S is a k-idempotent if e+e2=e2. Basic properties of k-regular semirings whose k-idempotents are commutative have been studied. © 2010 Springer Science+Business Media, LLC.