  In this article, we show that Mori domains, pseudo-valuation domains, and
$n$-absorbing ideals, the three seemingly unrelated notions in commutative ring
theory, are interconnected. In particular, we prove that an integral domain $R$
is a Mori locally pseudo-valuation domain if and only if each proper ideal of
$R$ is a finite product of 2-absorbing ideals of $R$. Moreover, every ideal of
a Mori locally almost pseudo-valuation domain can be written as a finite
product of 3-absorbing ideals. To provide concrete examples of such rings, we
study rings of the form $A+XB[X]$ where $A$ is a subring of a commutative ring
$B$ and $X$ is indeterminate, which is of independent interest, and along with
several characterization theorems, we prove that in such a ring, each proper
ideal is a finite product of $n$-absorbing ideals for some $n\ge 2$ if and only
if $A$ and $B$ are both Artinian reduced rings and the contraction map
$\text{Spec}(B)\to\text{Spec}(A)$ is a bijection. A complete description of
when an order of a quadratic number field is a locally pseudo valuation domain,
a locally almost pseudo valuation domain or a locally conducive domain is
given.
