We compare and contrast various relative cohomology theories that arise from resolutions
involving semidualizing modules. We prove a general balance result for relative …

A morphism f: M→ N of left R-modules is a phantom morphism if for any morphism g: A→ M,
with A finitely presented, the composition fg factors through a projective module …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

If R is an associative ring with identity, a theory of minimal flat resolutions is developed in the
category ((R-mod) op, Ab) of contravariant functors G:(R-mod) op→ Ab from the category R …

We investigate Tate cohomology of modules over a commutative noetherian ring with
respect to semidualizing modules. We identify classes of modules admitting Tate resolutions …

Let R be a commutative local Noetherian ring. We prove that the existence of a chain of
semidualizing R-complexes of length. d C 1/yields a degree-d polynomial lower bound for …

Let aa be an ideal in a commutative ring R. For an R-module M, we consider the small a a-
torsion Γ _ a (M)={x ∈ M ∣ ∃ n ∈ N: a^ n ⊆ (0: _Rx)\} Γ a (M)= x∈ M∣∃ n∈ N: an⊆(0: R …

Every duality between a full subcategory B of topological R-modules and a full subcategory
D of Mod-S which contains S and is closed under isomorphisms is determined in a natural …

A right R-module UR is said to be cotilting if Cog (UR)=⊥ UR, where⊥ UR= KerExt1R (, U).
So cotilting modules generalize injective cogenerators. If U is cotilting, then T=(KerHom …

We survey some recent developments in understanding homological properties of finitely
generated modules over a complete intersection. These properties mainly concern with …