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

In this paper, sufficient conditions for finitely generated modules over a commutative
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …

We will only assume some basic knowledge in module theory and category theory. In
particular, we will use the following notions that can be found in any textbook on modules or …

Let n be a positive integer, and let A be a strongly commutative differential graded (DG)
algebra over a commutative ring R. Assume that B= A [X 1,…, X n] is a polynomial extension …

Let R be a hereditary, indecomposable, left pure-semisimple ring. We show that R has finite
representation type if and only if a certain finitely presented module is endofinite, namely …

Motivated by a result of Araya, we extend the Auslander–Reiten duality theorem to Cohen–
Macaulay local rings. We also study the Auslander–Reiten conjecture, which is rooted in …

Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely
generated module is projective when certain Ext-modules vanish. But what if those Ext …

Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …

We study self-extensions of modules over symmetric artin algebras. We show that non-
projective modules with eventually vanishing self-extensions must lie in AR components of …

Let Λ be a Noetherian algebra and T∈ Λ-mod be an n-tilting module with Γ= End Λ (T). Then
Λ satisfies Auslander–Reiten conjecture if and only if so does Γ. As a consequence, we …