  Let $R$ be a commutative ring with nonzero identity. A. Yassine et al.
defined in the paper (Yassine, Nikmehr and Nikandish, 2020), the concept of
$1$-absorbing prime ideals as follows: a proper ideal $I$ of $R$ is said to be
a $1$-absorbing prime ideal if whenever $xyz\in I$ for some nonunit elements
$x,y,z\in R$, then either $xy\in I$ or $z\in\ I$. We use the concept of
$1$-absorbing prime ideals to study those commutative rings in which every
proper ideal is a product of $1$-absorbing prime ideals (we call them
$OAF$-rings). Any $OAF$-ring has dimension at most one and local $OAF$-domains
$(D,M)$ are atomic such that $M^2$ is universal.
