  Recently, many authors have embraced the study of certain properties of
modules such as projectivity, injectivity and flatness from an alternative
point of view. Rather than saying a module has a certain property or not, each
module is assigned a relative domain which, somehow, measures to which extent
it has this particular property. In this work, we introduce a new and fresh
perspective on flatness of modules. However, we will first investigate a more
general context by introducing domains relative to a precovering class $\x$. We
call these domains $\x$-precover completing domains. In particular, when $\x$
is the class of flat modules, we call them flat-precover completing domains.
This approach allows us to provide a common frame for a number of classical
notions. Moreover, some known results are generalized and some classical rings
are characterized in terms of these domains.
