Modules determined by their annihilator classes

Autores: Simion Breaz, Jan Trlifaj
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 1, 2010, págs. 225-240
Idioma: inglés
DOI: 10.1112/jlms/jdp065
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Resumen
- We present a classification of those finite length modules X over a ring A that are isomorphic to every module Y of the same length such that Ker(HomA(-,X)) = Ker(HomA(-, Y )), that is, 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 the case when A is 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.