Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 15, Number 2 (2013), 53-71.
Homological dimensions of ring spectra
We define homological dimensions for $S$-algebras, the generalized rings that arise in algebraic topology. We compute the homological dimensions of a number of examples, and establish some basic properties. The most difficult computation is the global dimension of real $K$-theory $KO$ and its connective version $ko$ at the prime 2. We show that the global dimension of $KO$ is 2 or 3, and the global dimension of $ko$ is 4 or 5.
Homology Homotopy Appl., Volume 15, Number 2 (2013), 53-71.
First available in Project Euclid: 8 November 2013
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Hovey, Mark; Lockridge, Keir. Homological dimensions of ring spectra. Homology Homotopy Appl. 15 (2013), no. 2, 53--71. https://projecteuclid.org/euclid.hha/1383945275