The discrete module category for the ring of K-theory operations

AbstractWe study the category of discrete modules over the ring of degree-zero stable operations in p-local complex K-theory, where p is an odd prime. We show that the K(p)-homology of any space or spectrum is such a module, and that this category is isomorphic to a category defined by Bousfield and used in his work on the K(p)-local stable homotopy category. We give a simple construction of cofree discrete modules and construct the analogue in the category of discrete modules of a four-term exact sequence due to Bousfield