Homology, Homotopy and Applications

Volume 7 (2005)

Number 1

Strict modules and homotopy modules in stable homotopy

Pages: 39 – 49

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n1.a3


Javier J. Gutiérrez (Departament d’ Álgebra i Geometria, Universitat de Barcelona, Spain)


Let $R$ be any associative ring with unit and let $HR$ denote the corresponding Eilenberg-Mac Lane spectrum. We show that the category of algebras over the monad $X \mapsto HR \wedge X$ on the homotopy category of spectra is equivalent to the homotopy category associated to a model category of $HR$-module spectra, if the ring $R$ is a field or a subring of the rationals, but not for all rings.


ring spectrum, module spectrum, derived category

2010 Mathematics Subject Classification

Primary 55P43. Secondary 18E30, 55P42.

Published 1 January 2005