  We use the concept of a regular object with respect to another object in an
arbitrary category, defined in \cite{dntd}, in order to obtain the transfer of
regularity in the sense of Zelmanowitz between the categories $R-$mod and
$S-$mod, when $S$ is an excellent extension of the ring $R$. Consequently, we
obtain a result of \cite{ps}: if $S$ is an excellent extension of the ring $R$,
then $S$ is von Neumann regular ring if and only if $R$ is also von Neumann
regular ring. In the second part, using relative regular modules, we give a new
proof of a classical result: the von Neumann regular property of a ring is
Morita invariant. Finally, the von Neumann regularity of the Morita ring is
investigated.
