  Sufficient conditions on a space are given which guarantee that the
$K$-theory ring and the ordinary cohomology ring with coefficients over a
principal ideal domain are invariants of, respectively, the adic genus and the
SNT set. An independent proof of Notbohm's theorem on the classification of the
adic genus of $BS^3$ by $KO$-theory $\lambda$-rings is given. An immediate
consequence of these results about adic genus is that the power series ring
$\mathbf{Z} \lbrack \lbrack x \rbrack \rbrack$ admits uncountably many pairwise
non-isomorphic $\lambda$-ring structures.
