Coulomb screening and weak interactions in a hot, magnetized plasma are investigated. Coulomb screening is evaluated in a relativistic thermal plasma in which electrons and positrons are in equilibrium. In addition to temperature effects, effects on weak screening from a strong external magnetic field are evaluated. In high fields, the electron transverse momentum components are quantized into Landau levels. The characteristic plasma screening length at high temperatures and at high magnetic fields is explored. In addition to changes to the screening length, changes in weak interaction rates are estimated. It is found that high fields can result in increased $beta$-decay rates as the electron and positron spectra are dominated by Landau levels. Finally, the effects studied here are evaluated in a simple r-process model. It is found that relativistic Coulomb screening has a small effect on the final abundance distribution. While changes in weak interaction rates in strong magnetic fields can have an effect on the r-process evolution and abundance distribution, the field strength required to have a significant effect may be larger than what is currently thought to be typical of the r-process environment in collapsar jets or neutron star mergers. If r-process sites exist in fields $gtrsim 10^{14}$ G effects from fields on weak decays could be significant.
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