Semisimple ring spectra

Mark Hovey and Keir Lockridge

Abstract. We define global dimension and weak dimension for the structured ring spectra
that arise in algebraic topology. We provide a partial classification of ring spectra of global
dimension 0, the semisimple ring spectra of the title. These 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.