| A Γ-semiring (M, +, α) whose additive reduct is a Γ-semilattice, is called a k-regular Γ -semiring if for each a ∈ M there exists x ∈ M such that a + aαxαa = aαxαa, α∈Γ. Here we introduce quasi k-ideals in Γ-semirings and characterize the k-regular Γ-semirings by their quasi k-ideals. |