Small ring spectra
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 \(X\).
scientific article; zbMATH DE number 64208