Homology, Homotopy and Applications
Volume 15 (2013)
Homological dimensions of ring spectra
Pages: 53 – 71
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.
ring spectrum, global dimension
2010 Mathematics Subject Classification
16E10, 18E30, 55P43