On characterization of minimal $k$-bi-ideals in $k$-regular and completely $k$-regular semirings

On the Semigroup of Bi-Ideals of an Ordered Semigroup

“…(2) If S is regular, then a nonempty subset B of S is a bi-ideal of S if and only if B = (RL] for some right ideal R and left ideal L of S (see [5]).…”