We characterize Ding modules and complexes over Ding-Chen rings. We show that, over a
Ding-Chen ring R, the Ding projective (respectively, Ding injective, respectively, Ding flat) R …

We consider two classes of modules over coherent rings: the Gorenstein FP-injective
modules, and the weakly Ding injective modules. The Gorenstein FP-injective modules are …

We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian
algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its …

Given a commutative Noetherian ring $ R $ with total ring of fractions $ Q (R) $, and a finitely
generated $ R $-submodule $ M $ of $ Q (R) $, we prove an equality between trace ideal …

We establish a prescribed upper bound for the projective dimension of a finitely generated
module over a Cohen-Macaulay local ring (with canonical module) satisfying certain …

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} …

Let ℰ be an injectively resolving subcategory of left R-modules. We study a particular case of
ℰ-Gorenstein injective and flat modules, called strongly ℰ-Gorenstein injective and flat …

A generalization of a theorem of Foxby Page 1 Arch. Math. 93 (2009), 123–127 c© 2009
Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020123-5 published online August 6, 2009 …

Two generalizations of Auslander-Reiten duality and applications Page 1 Two generalizations of
Auslander–Reiten duality and applications Arash Sadeghi and Ryo Takahashi …

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 …