Small ring spectra
type: Item
instance of: scholarly article
title: Small ring spectra
zbMATH Open document ID: 0759.55006
DOI: 10.1016/0022-4049(92)90131-X
author: Ethan S. Devinatz
published in: Journal of Pure and Applied Algebra
publication date: 1992-09-27T00:00:00Z
review text: Let \(X\) be a ring spectrum, i.e. a spectrum with a multiplication \(\mu: X\wedge X\to X\) and a left unit \(\eta: S^ 0\to X\) in the stable homotopy category, and \(f:\Sigma^{2k}X\to X\) a self-map of \(X\). The author presents conditions which imply that the cofibre \(C(f^ 2)\) of \(f^ 2:\Sigma^{4k}X\to X\) is a ring spectrum such that the inclusion map \(X\to C(f^ 2)\) is a map of ring spectra. This result is applied to show that the cofibre of a sufficiently large iterate of any \(v_ n\) self-map of a \(p\)-local finite ring spectrum \(X\) has itself a ring structure extending the one of \(X\).
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 64208
zbMATH Keywords: ring spectrum
zbMATH Keywords: stable homotopy category
zbMATH Keywords: \(v_ n\) self-map
reviewed by: Rainer Vogt
MaRDI profile type: Publication
cites work: Q4067782
cites work: K-Theory and the Generating Hypothesis
cites work: Q3805461
cites work: Q3049513
description: scientific article; zbMATH DE number 64208