Multiplicative structures on Moore spectra

TL;DR

This paper establishes the existence of multiplicative structures of varying levels on Moore spectra, showing that certain spectra admit $ ext{E}_n$-algebra structures depending on their construction parameters.

Contribution

It proves that Moore spectra of specific types and at various primes can be endowed with $ ext{E}_n$-algebra structures, extending previous understanding of their multiplicative properties.

Findings

$ ext{S}/8$ is an $ ext{E}_1$-algebra

$ ext{S}/32$ is an $ ext{E}_2$-algebra

Existence of generalized Moore spectra of type $h$ with $ ext{E}_n$-algebra structures

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.