  In this paper, we study black strings in asymptotic safety gravity (ASG)
scenario. The ASG approach is introduced by implementing gravitational and
cosmological running coupling constants directly in the black string metric. We
calculate the Hawking temperature, entropy, and heat capacity of the improved
black string metric in two cases: considering the cosmological constant fixed
in some fixed point and the general case where both Newton's constant and
cosmological constant are improved. For the identification of the scale moment
we used an general inverse law setting $k(r)\sim 1/r^{n}$. We show that
improving only the Newton's constant the problem of singularity is solved for
the identifications with $n>1$. However, if the cosmological constant is also
running the singularity persists in the solution. Also, we show that the ASG
effects predicts the presence of a remnant mass in the final evaporation
process. Besides that, a logarithmic correction is observed in the entropy.
However, a running cosmological constant introduces new correction terms to the
entropy beyond that. We show that the improved black string solution remains
stable, as in the usual case. Phase transitions are not observed in both cases
studied here.
