Homological aspects of semidualizing modules
By Ryo Takahashi, D. White. 2007
135 citations recorded by the source corpus.
We investigate the notion of the $C$-projective dimension of a module, where $C$ is a semidualizing module. When $C=R$, this recovers the standard projective dimension. We show that three natural definitions of finite $C$-projective dimension agree, and investigate the relationship between relative cohomology modules and absolute cohomology modules in this setting. Finally, we prove several results that demonstrate the deep connections between modules of finite projective dimension and modules of finite $C$-projective dimension. In parallel, we develop the dual theory for injective dimension and $C$-injective dimension.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fc3fb5528c71f35e785d32d8d61cfa4bd7f801b2
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Proper Resolutions and Gorenstein Categories (2012, background): “Gorenstein projective and injective modules and some related generalized versions have been studied by many authors, see [1,4,6–8,10–21], and the literatures listed in them.”
- Tate cohomology with respect to semidualizing modules (2009, background): “The next lemma is from an early version of [21].”
- Gorenstein projective dimension with respect to a semidualizing module (2006, methodology): “The tools developed in this paper have been particularly useful for investigating the similarities and differences between certain relative cohomology theories [15, 16 ] and the stability properties of operators on categories [17].”