  A matching in a hypergraph $\mathcal{H}$ is a set of pairwise disjoint
hyperedges. The matching number $\nu(\mathcal{H})$ of $\mathcal{H}$ is the size
of a maximum matching in $\mathcal{H}$. A subset $D$ of vertices of
$\mathcal{H}$ is a dominating set of $\mathcal{H}$ if for every $v\in
V\setminus D$ there exists $u\in D$ such that $u$ and $v$ lie in an hyperedge
of $\mathcal{H}$. The cardinality of a minimum dominating set of $\mathcal{H}$
is the domination number of $\mathcal{H}$, denoted by $\gamma(\mathcal{H})$. It
was proved that $\gamma(\mathcal{H})\leq (r-1)\nu(\mathcal{H})$ for $r$-uniform
hypergraphs and the 2-uniform hypergraphs (graphs) achieving equality
$\gamma(\mathcal{H})=\nu(\mathcal{H})$ have been characterized. In this paper
we generalize the inequality $\gamma(\mathcal{H})\leq (r-1)\nu(\mathcal{H})$ to
arbitrary hypergraph of rank $r$ and we completely characterize the extremal
hypergraphs $\mathcal{H}$ of rank $3$ achieving equality
$\gamma(\mathcal{H})=(r-1)\nu(\mathcal{H})$.
