کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6425772 | 1633844 | 2013 | 41 صفحه PDF | دانلود رایگان |
Let (A;E) be an exact category and FâExt a subfunctor. A morphism Ï in A is an F-phantom if the pullback of an E-conflation along Ï is a conflation in F. If the exact category (A;E) has enough injective objects and projective morphisms, it is proved that an ideal I of A is special precovering if and only if there is a subfunctor FâExt with enough injective morphisms such that I is the ideal of F-phantom morphisms. A crucial step in the proof is a generalization of Salce's Lemma for ideal cotorsion pairs: if I is a special precovering ideal, then the ideal cotorsion pair (I,Iâ¥) generated by I in (A;E) is complete. This theorem is used to verify: (1) that the ideal cotorsion pair cogenerated by the pure-injective modules of R-Mod is complete; (2) that the ideal cotorsion pair cogenerated by the contractible complexes in the category of complexes Ch(R-Mod) is complete; and, using Auslander and Reiten's theory of almost split sequences, (3) that the ideal cotorsion pair cogenerated by the Jacobson radical Jac(Î-mod) of the category Î-mod of finitely generated representations of an Artin algebra is complete.
Journal: Advances in Mathematics - Volume 244, 10 September 2013, Pages 750-790