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math.RT2026
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…
math.RT2026
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…
math.RT2025
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…