Two filtration results for modules with applications to the Auslander condition
Volume 158 / 2019
Colloquium Mathematicum 158 (2019), 157-181 MSC: 18G25, 16E10, 16E30. DOI: 10.4064/cm7678-10-2018 Published online: 29 July 2019
Under some strong cograde conditions, we obtain two different filtrations of modules in terms of the properties of cotransposes of modules with respect to a semidualizing bimodule. Then we apply these filtrations to investigate the relationship between artin algebras satisfying the Auslander condition and Gorenstein algebras, which is related to a conjecture of Auslander and Reiten.