We study the role of environment in the evolution of galaxies up to z = 0.7 using the final zCOSMOS-bright data set. We use the colour as a proxy for the quenched population, and measure the dependence of the red fraction of galaxies on stellar mass and two environmental indicators: the local overdensity of galaxies δ and a demarcation of galaxies to centrals and satellites. The analysis is carried out by quantifying the role of different quenching processes. We find that the measured dependence of the red fraction of galaxies on stellar mass and environment can be well described by two quenching processes: one related only to stellar mass (mass quenching) and the other related to the local environment (environment quenching). Within the errors, these processes are independent of each other, and consistent with the z ~ 0 measurement. Moreover, the red fraction of centrals fr,cen
(both singleton centrals and centrals in the groups) does not show any trend with δ and more than 95% of fr,cen
is consistent with being produced through the mass quenching alone. The satellite galaxies are redder than the centrals at the same stellar mass and δ, requiring additional environment quenching. Given the observed fractional distribution of satellites at different overdensities, the normalized excess in the red fraction of satellites with respect to the red fraction of centrals is consistent with a scenario in which the satellites account for most of the δ-dependences observed in the overall population of galaxies covering 0.1 < z < 0.7.