  The notion of trivial extension of a ring by a module has been extensively
studied and used in ring theory as well as in various other areas of research
like cohomology theory, representation theory, category theory and homological
algebra. In this paper we extend this classical ring construction by
associating a ring to a ring $R$ and a family $M=(M_i)_{i=1}^{n}$ of $n$
$R$-modules for a given integer $n\geq 1$. We call this new ring construction
an $n$-trivial extension of $R$ by $M$. In particular, the classical trivial
extension will be just the $1$-trivial extension. Thus we generalize several
known results on the classical trivial extension to the setting of $n$-trivial
extensions and we give some new ones. Various ring-theoretic constructions and
properties of $n$-trivial extensions are studied and a detailed investigation
of the graded aspect of $n$-trivial extensions is also given. We end the paper
with an investigation of various divisibily properties of $n$-trivial
extensions. In this context several open questions arise.
