2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142739We provide a new algebraic description of the structure on the set of all unstable cohomology operations for a suitable generalised cohomology theory, E^*. Our description is as a graded and completed version of a Tall-Wraith monoid. The E^*-cohomology of a space X is a module for this Tall-Wraith monoid. We also show that the corresponding Hopf ring of unstable co-operations is a module for the Tall-Wraith monoid of unstable operations. Further examples are provided by considering operations from one theory to another.61 pages, no figures; uses xy, pxfontsAlgebraic TopologyK-Theory and HomologyRings and Algebras55S25; 55N20; 16W99text