… generated homology, Christensen introduced the dimension G-… bounded and finitely generated
homology. To circumvent … homological dimension based on a larger class of complexes…

… Totushek, Using semidualizing complexes to detect Gorenstein rings, Arch. Math. (Basel) …
Yassemi, Modules of finite homological dimension with respect to a semidualizing module, Arch…

… An X -resolution of M is a complex of R-modules in X of the form X = ⋯ → ∂ 2 X X 1 → …
homological dimension and call it the projective dimension of M. Similarly, the injective dimension …

… semidualizing complexes with finite injective dimension. It is known that a homologically
bounded complex X with finitely generated homology … consider a semidualizing complex C with …

… complex (known as a “semi-dualizing complex” in the literature) interpolates between those
of a dualizing and a dedualizing complex. … same up to finite homological dimension”, and so …

We introduce and study a class of objects that encompasses Christensen and Foxby’s
semidualizing modules and complexes and Kubik’s quasi-dualizing modules: the class of 𝔞 -adic …

… Are the conditions on C to be semidualizing necessary so that the relative homological
dimensions preserve their properties? If not, what are the minimum necessary conditions? …

… The relative homological theory goes back to Butler and Horrocks [4], and Eilenberg and …
tively, GC-injective) complexes, where C is a semidualizing module over a commutative ring, …

… results of homological algebra to the relative setting with respect to a semidualizing module…
For instance, this has been done for the classical and Gorenstein homological dimensions …

… of \(\infty \)-tilting theory in [25] and applied to pseudo-dualizing complexes of bimodules
in [23]. The latter are otherwise known as “semi-dualizing complexes” in the literature [2, 12]. …