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HOMOLOGICAL ASPECTS OF SEMIDUALIZING MODULES
, 2007
"... Abstract. We investigate the notion of the Cprojective 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 Cprojective dimension agree, and investigate the relationship between relat ..."
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Abstract. We investigate the notion of the Cprojective 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 Cprojective 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 Cprojective dimension. In parallel, we develop the dual theory for injective dimension and Cinjective dimension.