An element a of a semigroupSis a left magnifier if λa, the inner left translation associated with a, is surjective and is not injective (E. S. Ljapin [11]). When this happens there exists a proper subsetMofSsuch that the restriction toMof λais bijective. In that caseMis said to bea minimal subset for the left magnifier a(F. Migliorini [13], [14], [15]). Remark that ifSis a semigroup having left identities then every left magnifier ofSadmits minimal subsets which are right ideals. Characterisations for semigroups with left magnifiers which also contain left identities have been given by E. S. Ljapin and R. Desq, using the bicyclic monoid. The general problem, precisely to give a characterization of semigroups having left magnifiers, is still open.