2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61523Sufficient 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 $λ$-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 $λ$-ring structures.16 pagesAlgebraic Topology55P15; 55N15, 55P60, 55S25text