E. G. Šutov [3] and N. Kimura, T. Tamura and R. Merkel [2] considered $\lambda$-semigroups, i.e. semigroups in which every subsemigroup is a left ideal. S.Bogdanovic and the author treated in [1] $\lambda_n$-semigroups, i.e. semigroups in which \[ S^nA=A^{n+1} \] for every subsemigroup $A$ of $S$. In this paper we generalize the results from [1]. We prove that $S$ is an $\mathfrak L_n$-semigroup if and only if $S$ is a retractive extension of a right zero band by an $\mathfrak L_n$-nil-semigroup (Th. 3,4).