5 citations · 21 across the 43 of their papers we have counts for
53 papers
Regularity, local cohomology and injective modules under contracting endomorphisms
Kamran Divaani-Aazar, Mohammad Eghbali
This work extends several fundamental results previously established for rings of characteristic to the broader class of rings that admit a contracting endomorphism. Specifical…
Equivalence classes of Wakamatsu tilting modules and preenveloping and precovering subcategories
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
Let R be an associative ring with identity. We introduce an equivalence relation on the class of Wakamatsu tilting right R modules. By using this equivalence relation, we extend th…
Cotilting invariance of the Auslander-Reiten conjecture
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
Let R be an associative ring with identity, and let T be a tilting right R-module, with S=End(T). It is known that if R is a Noetherian algebra that satisfies the Auslander-Reiten…
Comparing four definitions of cotilting modules
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
In contrast to the theory of tilting modules, the dual theory lacks a unified definition. Nevertheless, several notions of cotilting modules have been proposed. In this paper, we c…
Cotilting modules and Gorenstein homological dimensions
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
For a dualizing module over a commutative Noetherian ring with identity, it is known that its Auslander class (respectively, Bass class $\math…
On the Wakamatsu tilting conjecture
Kamran Divaani-Aazar, Ali Mahin Fallah, Massoud Tousi
Let R be an associative ring with identity. We establish that the generalized Auslander-Reiten conjecture implies the Wakamatsu tilting conjecture. Furthermore, we prove that any W…