  In this work, we study the relation of cosmic environment and morphology with
the star-formation (SF) and the stellar population of galaxies. Most
importantly, we examine if this relation differs for systems with active and
non-active supermassive black holes. For that purpose, we use 551 X-ray
detected active galactic nuclei (AGN) and 16,917 non-AGN galaxies in the
COSMOS-Legacy survey, for which the surface-density field measurements are
available. The sources lie at redshift of $\rm 0.3<z<1.2$, probe X-ray
luminosities of $\rm 42<log\,[L_{X,2-10keV}(erg\,s^{-1})]<44$ and have stellar
masses, $\rm 10.5<log\,[M_*(M_\odot)]<11.5$. Our results show that isolated AGN
(field) have lower SFR compared to non AGN, at all L$_X$ spanned by our sample.
However, in denser environments (filaments, clusters), moderate L$_X$ AGN ($\rm
log\,[L_{X,2-10keV}(erg\,s^{-1})]>43$) and non-AGN galaxies have similar SFR.
We, also, examine the stellar populations and the morphology of the sources in
different cosmic fields. For the same morphological type, non-AGN galaxies tend
to have older stellar populations and are less likely to have undergone a
recent burst in denser environments compared to their field counterparts. The
differences in the stellar populations with the density field are, mainly,
driven by quiescent systems. Moreover, low L$_X$ AGN present negligible
variations of their stellar populations, in all cosmic environments, whereas
moderate L$_X$ AGN have, on average, younger stellar populations and are more
likely to have undergone a recent burst, in high density fields. Finally, in
the case of non-AGN galaxies, the fraction of bulge-dominated (BD) systems
increases with the density field, while BD AGN are scarce in denser
environments. Our results are consistent with a scenario in which a common
mechanism, such as mergers, triggers both the SF and the AGN activity.
