Embedding modules of finite homological dimension

Details Embedding modules of finite homological dimension Embedding modules of finite homological dimension

2012-01-14

arxiv.org/abs/1201.3037v1

Mathematics

Commutative Algebra

12 pages, to appear in Glasgow Math. J

Scientific paper

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.

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