TY - JOUR
AU - Takahashi, Ryo
AU - White, Diana
PY - 2010/03/01
Y2 - 2022/12/06
TI - Homological aspects of semidualizing modules
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 106
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-15121
UR - https://www.mscand.dk/article/view/15121
SP - 5-22
AB - 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.
ER -