  The so called Pr\"ufer $v$-multiplication domains (P$v$MD's) are usually
defined as domains whose finitely generated nonzero ideals are $t$-invertible.
These domains generalize Pr\"ufer domains and Krull domains. The P$v$MD's are
relatively obscure compared to their very well known special cases. One of the
reasons could be that the study of P$v$MD's uses the jargon of star operations,
such as the $v$-operation and the $t$-operation. In this paper, we provide
characterizations of and basic results on P$v$MD's and related notions without
star operations.
