Let R and S be rings and S C R a semidualizing bimodule. We investigate the relative Tor
functors Tor i ℳ ℒ C ( − , − ) $\text {Tor}_{i}^{\mathcal {M}\mathcal {L}_{C}}(-,-)$ defined via C-…

… In this section, C is a semidualizing R-module, and M and N are R-modules. The results
of this section document some properties of proper FC-resolutions and proper PC-resolutions, …

… In this paper, we investigate semi dualizing modules and associated relative cohomology
functors. … class with respect to C, denoted sic or sic(R), consists of all Ä-modules Μ satisfying …

… duality properties with respect to a rank 1 free module that gives rise to the Gorenstein dimension
[3], [4]. A free … , then for each mA-primary ideal I there is an equality of Hilbert functions …

… provide a Yoneda-type description of the first relative Ext functor. Finally, we show by example
that each distinct relative cohomology construction does in fact result in a different functor. …

… We denote by mod-R the category of finitely presented R-modules and by (modR, Ab) the
functor … White, Gorenstein projective dimension with respect to a semidualizing module, …

… functors and relative homology functors. Finally, motivated by the idea of Sather–Wagstaff
et al. [Comparison of relative cohomology theories with respect to semidualizing … module by …

… BC (S) with respect to a semidualizing bimodule C contains all FP-injective S-modules. We
… right IC (R)-resolutions of R-modules by left derived functors Extn(−, −) over a left Noetherian …

… finite modules over commutative Noetherian rings with respect to a semidualizing module; …
, R) to indicate the duality functor with respect to R, or simply the duality functor. For every R-…

… R-module is C-projective, where C is a semidualizing R-module. … some kernel subcategories
related to C-tilting modules. … : Relative Tor functors with respect to a semidualizing module. …