New York Journal of Mathematics
Volume 15 (2009) 219-243


Mark Hovey and Keir Lockridge

Semisimple ring spectra

Published: June 1, 2009
Keywords: Ring spectrum, semisimple, von Neumann regular, triangulated category, quasi-Frobenius ring, IF-ring, generating hypothesis
Subject: Primary: 55P43; Secondary: 18E30, 16E10

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 zero, 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.

Author information

Mark Hovey:
Department of Mathematics, Wesleyan University, Middletown, CT 06459

Keir Lockridge:
Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109