## Homology, Homotopy and Applications

### Homological dimensions of ring spectra

#### 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

https://projecteuclid.org/euclid.hha/1383945275

Mathematical Reviews number (MathSciNet)
MR3117386

Zentralblatt MATH identifier
1296.55013

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