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 and Applications, Vol. 15 (2013), No. 2, pp.53-71.
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