Quotients of even rings

Abstract

We prove that if $R$ is an ${\mathbb{E}}_2$-ring with homotopy concentrated in even degrees, and $\{x_j\}$ is any sequence of elements in ${\pi }_{2\ast }(R)$, then $R/(x_1,x_2,\cdots )$ admits the structure of an ${\mathbb{E}}_1$-$R$-algebra. This removes an assumption, common in the literature, that $\{x_j\}$ be a regular sequence.

3 pages; comments welcome!