We examine the star formation rates (SFRs) of galaxies in a redshift slice encompassing the z=0.834 cluster RX J0152.7-1357. We used a low-dispersion prism in the Inamori Magellan Areal Camera and Spectrograph (IMACS) to identify galaxies with z<23.3 AB mag in diverse environments around the cluster out to projected distances of ~8 Mpc from the cluster center. We utilize a mass-limited sample (M>2x10^{10} M_sun) of 330 galaxies that were imaged by Spitzer MIPS at 24 micron to derive SFRs and study the dependence of specific SFR (SSFR) on stellar mass and environment. We find that the SFR and SSFR show a strong decrease with increasing local density, similar to the relation at z~0. Our result contrasts with other work at z~1 that find the SFR-density trend to reverse for luminosity-limited samples. These other results appear to be driven by star-formation in lower mass systems (M~10^{10} M_sun). Our results imply that the processes that shut down star-formation are present in groups and other dense regions in the field. Our data also suggest that the lower SFRs of galaxies in higher density environments may reflect a change in the ratio of star-forming to non-star-forming galaxies, rather than a change in SFRs. As a consequence, the SFRs of star-forming galaxies, in environments ranging from small groups to clusters, appear to be similar and largely unaffected by the local processes that truncate star-formation at z~0.8.
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