  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 $\pi_{2*}(R)$, 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.
