  In this paper we study a family of scattered $\F_q$--linear sets of rank $tn$
of the projective space $PG(2n-1,q^t)$ ($n \geq 1$, $t\geq 3$), called of {\it
pseudoregulus type}, generalizing results contained in [G. Marino, O.
Polverino, R. Trombetti: On ${\mathbb F}_q$--linear sets of $\PG(3,q^3)$ and
semifields, {\em J. Combin. Theory Ser. A}, {\bf 114} (2007), 769--788] and in
[M. Lavrauw, G. Van de Voorde: Scattered linear sets and pseudoreguli,
preprint]. As an application, we characterize, in terms of the associated
linear sets, some classical families of semifields: the Generalized Twisted
Fields and the 2-dimensional Knuth semifields.
