Cotilting modules over tame hereditary algebras.
This paper discusses cotilting modules of injective dimension at most one over a finite-dimen\-sion\-al algebra. In the first part of the paper, the authors establish, for a left Noetherian ring \(\Lambda\), a bijective correspondence between equivalence classes of (possibly infinitely generated) cotilting \(\Lambda\)-modules and torsion pairs \((T,F)\) for the category of finitely generated \(\Lambda\)-modules with \(\Lambda\in F\). In the second part, the authors give a complete classification of all cotilting modules over a tame hereditary Artin algebra. Cotilting modules are pure-injective, and their arguments make use of the well-known classification of indecomposable pure-injective modules over tame hereditary Artin algebras.
scientific article; zbMATH DE number 2101098