Publication at Faculty of Mathematics and Physics |
2010
Abstract
We present a classification of those finite length modules X over a ring A which are isomorphic to every module Y of the same length such that Ker Hom(-,X) = Ker Hom (-,Y), i.e., X is determined by its length and the torsion pair cogenerated by X. We also prove the dual result using the torsion pair generated by X.
For A right hereditary, we prove an analogous classification using the cotorsion pair generated by X, but show that the dual result is not provable in ZFC.