Comparing four definitions of cotilting modules

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 compare four of the main definitions of cotilting modules that have appeared in the literature. We show that, in the setting of finitely generated right modules, three of these definitions coincide over right Artinian Noetherian algebras, and all four coincide over Artin algebras.