Multiplicative structures on Moore spectra

Abstract

In this article we show that $\mathbb{S}/8$ is an ${\mathbb{E}}_1$-algebra, $\mathbb{S}/32$ is an ${\mathbb{E}}_2$-algebra, $\mathbb{S}/p^{n+1}$ is an ${\mathbb{E}}_n$-algebra at odd primes and, more generally, for every $h$ and $n$ there exist generalized Moore spectra of type $h$ which admit an ${\mathbb{E}}_n$-algebra structure.

13 pages. v2: added an appendix on bar-cobar duality. Comments welcome!