Resolutions and Semidualizing Modules
Feickert, Aaron James
MetadataShow full item record
Projective and injective modules are of key importance in algebra, in part because of their useful homological properties. The notion of C-projective and C-injective modules generalizes these constructions. In particular, these modules may be used to construct resolutions and define related homological dimensions in a natural way. When C is a semidualizing module, the C-projective and C-injective modules have particularly useful homological properties. Further, one may combine projective and C-projective resolutions to construct complete PC-resolutions (and, dually, complete IC-resolutions) that yield other modules with nice homological properties. This paper surveys some of the literature on these constructions.