Strict modules and homotopy modules in stable homotopy

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.

Keywords

ring spectrum, module spectrum, derived category

2010 Mathematics Subject Classification

Primary 55P43. Secondary 18E30, 55P42.

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Published 1 January 2005