An integral domain is called almost perfect if all its proper quotients are perfect rings; such domains are necessarily one-dimensional. This paper studies a higher-dimensional generalization of almost perfect domains via the Formula: see text-operation. We define a Formula: see text-almost perfect domain as a domain Formula: see text for which the Formula: see text-factor ring Formula: see text of Formula: see text is a perfect ring for every nonzero Formula: see text-ideal Formula: see text of Formula: see text. The class of Formula: see text-almost perfect domains properly contains almost perfect domains, Krull domains, and strong Mori domains of Formula: see text-dimension one. Several characterizations of Formula: see text-almost perfect domains are established. In particular, it is proved that a domain Formula: see text is Formula: see text-almost perfect if and only if it is of finite Formula: see text-character and Formula: see text-locally almost perfect. A module-theoretic characterization of Formula: see text-almost perfect domains is given by using the notion of Formula: see text-semi-artinian modules: a domain Formula: see text is Formula: see text-almost perfect precisely when its quotient module Formula: see text is Formula: see text-semi-artinian and Formula: see text is Formula: see text-local, where Formula: see text is the quotient field of Formula: see text and Formula: see text is the hereditary torsion theory induced by the Formula: see text-operation. Furthermore, in order to provide some original examples, we also characterize Formula: see text-almost perfect domains in certain types of pullback constructions. Finally, we show that a domain Formula: see text is a Krull domain if and only if Formula: see text is a Prüfer Formula: see text-multiplication domain which is Formula: see text-almost perfect, and that every Formula: see text-almost perfect domain is a Formula: see text-Matlis domain.
Lei et al. (Thu,) studied this question.