On \(B^*\)-pure semigroups
Let S be a semigroup. A bi-ideal A of S is called B-pure if \(A\cap xS=xA\) and \(A\cap Sx=Ax\) for all \(x\in S\). By making use of a criterion due to the reviewer [Acta Sci. Math. 33, 315-317 (1972; Zbl 0247.20072)] the author proves that every bi-ideal of S is B-pure if and only if \(S^ 2\) is a semilattice of groups.
scientific article; zbMATH DE number 3849503