Semisimple ring spectra (Q1019605)

The authors define global dimension and weak dimension for the structured ring spectra that arise in algebraic topology. They provide a partial classification of ring spectra of global dimension 0 (called semisimple ring spectra). These semisimple ring spectra are closely related to classical rings whose projective modules admit the structure of a triangulated category. Applications to two analogues of the generating hypothesis in algebraic topology are given.