Let R be a ring, let G be a countable amenable group and let RG be a crossed product. The
goal of this paper is to construct, starting with a suitable length function L on the category of
left modules over R, a length function on a subcategory of the category of left modules over
RG, which coincides with the whole category if LpRRqă8. This construction can be
performed using a dynamical invariant associated with the original length function L, called
algebraic L-entropy. We apply our results to two classical problems on group rings: the …