We investigate the interplay between properties of Ext modules and the ascent of module
structures along local ring homomorphisms. Specifically, let $\varphi\colon (R,\mathfrak {m} …

Suppose (R, m) and (S, n) are commutative Noetherian local rings and ϕ: R→ S is a flat
local homomorphism with the property that the induced homomorphism R/m→ S/mS is …

Given a flat local ring homomorphism R → SR→ S and two finitely generated R-modules M
and N, we describe conditions under which the modules\rm Tor^ R _ i (M, N) Tor i R (M, N) …

Let $ R $ be a commutative ring and let $ S $ be an $ R $-algebra. It is well-known that if $ N
$ is an injective $ R $-module, then $\operatorname {Hom} _R (S, N) $ is an injective $ S …

A morphism f: M→ N f:M→N of left R-modules is called an n-phantom morphism (resp. a Tor
n-epimorphism) if the induced morphism Tor n (A, f)= 0 (resp. Tor n (A, f) is an epimorphism) …

Stable cohomology is a generalization of Tate cohomology to associative rings, first defined
by Pierre Vogel. For a commutative local ring R with residue field k, stable cohomology …

The notion of $\mathcal {K} $-extending modules was defined recently as a proper
generalization of both extending modules and Rickart modules. Let $ M $ be a right $ R …

For a flat $ R-$ module $ F, $ we prove that $\operatorname {Hom} _ {R}(F,-) $ is a functor
from the category of linearly compact $ R-$ modules to itself and is exact. Moreover …

Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

Classically, the Auslander–Bridger transpose finds its best applications in the well-known
setting of finitely presented modules over a semiperfect ring. We introduce a class of …