Homology, Homotopy and Applications

Volume 15 (2013)

Number 2

Homological dimensions of ring spectra

Pages: 53 – 71

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n2.a3


Mark Hovey (Department of Mathematics, Wesleyan University, Middletown, Conn., U.S.A.)

Keir Lockridge (Department of Mathematics, Gettysburg College, Gettysburg, Penn., U.S.A.)


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

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Published 4 December 2014