On the Generalized Auslander–Reiten Conjecture under Certain Ring Extensions Page 1
Canad. Math. Bull. Vol. 58 (1), 2015 pp. 134–143 http://dx.doi.org/10.4153/CMB-2014-052-9 c …

Let A be a finite dimensional algebra over field K and X a finitely generated A-module. X is
said to be reflexive (resp. torsionless) if the canonical map σ X: X→ X** is an isomorphism …

We study modules over a commutative artin local ring R. For the most part, we concentrate
on almost split sequences with uniserial modules in its end terms. Based on our …

Let R be a Cohen-Macaulay local ring of dimension d with canonical module ωR. In this
article we extend Auslander-Reiten duality theorem to certain R-algebras. As a …

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 …

In this paper, we introduce the notion of excellent extensions of rings. Let Γ be an excellent
extension of an Artin algebra Λ, we prove that Λ satisfies the Gorenstein symmetry …

Let G be a subgroup of the automorphism group of a commutative ring with identity T. Let R
be a subring of T. We show that RG⊂ TG is a minimal ring extension whenever R⊂ T is a …

Over a commutative Noetherian ring, we show that Auslander-Reiten conjecture holds true
for the class of (finitely generated) modules whose dual has finite complete intersection …

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 …

Let kG be the group algebra of a finite group G over a field k of characteristic p, where p is a
prime. Fix a non-trivial normal p-subgroup Q of G. In this paper, we study Auslander-Reiten …