$\lambda$-rings are algebras over some ring?

Question

Let us call $\lambda$-ring what is sometimes called special $\lambda$-ring (there are axioms for product and composition, not only sum). Is it true that they are algebras over some ring like symmetric functions $\mathrm{Symm}$ (with some other ring structure, not induced from $\mathrm{Symm} \simeq \mathbb Z[h_1, h_2, \ldots]$), or $\mathrm{End}(\mathrm{Symm})$ (which is usually only group), or whatever?