  A linearized polynomial $f(x)\in\mathbb F_{q^n}[x]$ is called scattered if
for any $y,z\in\mathbb F_{q^n}$, the condition $zf(y)-yf(z)=0$ implies that $y$
and $z$ are $\mathbb F_{q}$-linearly dependent. In this paper two
generalizations of the notion of a scattered linearized polynomial are defined
and investigated. Let $t$ be a nontrivial positive divisor of $n$. By weakening
the property defining a scattered linearized polynomial, L-$q^t$-partially
scattered and R-$q^t$-partially scattered linearized polynomials are introduced
in such a way that the scattered linearized polynomials are precisely those
which are both L-$q^t$- and R-$q^t$-partially scattered. Also, connections
between partially scattered polynomials, linear sets and rank metric codes are
exhibited.
