  This paper builds on work of Hochster and Yao that provides nice embeddings
for finitely generated modules of finite G-dimension, finite projective
dimension, or locally finite injective dimension. We extend these results by
providing similar embeddings in the relative setting, that is, for certain
modules of finite G_C-dimension, finite P_C-projective dimension, locally
finite GI_C-injective dimension, or locally finite I_C-injective dimension
where C is a semidualizing module. Along the way, we extend some results for
modules of finite homological dimension to modules of locally finite
homological dimension in the relative setting.
