EMBEDDING MODULES OF FINITE HOMOLOGICAL DIMENSION

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.