  The main purpose of this paper is to define dynamical degrees for rational
maps over an algebraic closed field of characteristic zero and prove some basic
properties (such as log-concavity) and give some applications. We also define
relative dynamical degrees and prove a "product formula" for dynamical degrees
of semi-conjugate rational maps in the algebraic setting. The main tools are
the Chow's moving lemma and a formula for the degree of the cone over a
subvariety of $\mathbb{P}^N$. The proofs of these results are valid as long as
resolution of singularities are available (or more generally if appropriate
birational models of the maps under consideration are available). This
observation is applied for the cases of surfaces and threefolds over a field of
positive characteristic.
