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International Press, Homology, Homotopy and Applications, 2(15), p. 53-71

DOI: 10.4310/hha.2013.v15.n2.a3

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Homological dimensions of ring spectra

Journal article published in 2010 by Mark Hovey, Keir Lockridge
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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 1, 2, or 3, and the global dimension of ko is 4 or 5. Comment: 16 pages