Comment on: "Bi-interior ideals of semigroups".

This is about the paper "Bi-interior ideals of semigroups" by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. 38 (2018) 69–78. According to Theorem 3.11 (also Theorem 3.3(8)) of the paper, the intersection of a bi-interior ideal B of a semigroup M and a subsemigroup A of M is a bi-interior ideal of M. Regarding to Theorem 3.6, every bi-interior ideal of a regular semigroup is an ideal of M. We give an example that the above two results are not true for semigroups. According to the same paper, if M is a regular semigroup then, for every bi-interior ideal B , every ideal I and every left ideal L of S , we have B ∩ I ∩ L ⊆ B I L. The proof is wrong, we provide the corrected proof. In most of the results of the paper the assumption of unity is not necessary. Care should be taken about the proofs in the paper. [ABSTRACT FROM AUTHOR]