Homology, Homotopy and Applications

Homological dimensions of ring spectra

Mark Hovey and Keir Lockridge

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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 2 or 3, and the global dimension of $ko$ is 4 or 5.

Article information

Source
Homology Homotopy Appl., Volume 15, Number 2 (2013), 53-71.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hha/1383945275

Mathematical Reviews number (MathSciNet)
MR3117386

Zentralblatt MATH identifier
1296.55013

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 16E10: Homological dimension 18E30: Derived categories, triangulated categories

Keywords
Ring spectrum global dimension

Citation

Hovey, Mark; Lockridge, Keir. Homological dimensions of ring spectra. Homology Homotopy Appl. 15 (2013), no. 2, 53--71. https://projecteuclid.org/euclid.hha/1383945275


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