  We present reverberation mapping results for the MgII 2800 A broad emission
line in a sample of 193 quasars at 0.35<z<1.7 with photometric and
spectroscopic monitoring observations from the Sloan Digital Sky Survey
Reverberation Mapping project during 2014 - 2017. We find significant time lags
between the MgII and continuum lightcurves for 57 quasars and define a "gold
sample" of 24 quasars with the most reliable lag measurements. We estimate
false-positive rates for each lag that range from 1-24%, with an average
false-positive rate of 11% for the full sample and 8% for the gold sample.
There are an additional ~40 quasars with marginal MgII lag detections which may
yield reliable lags after additional years of monitoring. The MgII lags follow
a radius -- luminosity relation with a best-fit slope that is consistent with
alpha=0.5 but with an intrinsic scatter of 0.36dex that is significantly larger
than found for the Hb radius -- luminosity relation. For targets with SDSS-RM
lag measurements of other emission lines, we find that our MgII lags are
similar to the Hb lags and ~2-3 times larger than the CIV lags. This work
significantly increases the number of MgII broad-line lags and provides
additional reverberation-mapped black hole masses, filling the redshift gap at
the peak of supermassive black hole growth between the Hb and CIV emission
lines in optical spectroscopy.
