کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425772 1633844 2013 41 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Ideal approximation theory
ترجمه فارسی عنوان
تئوری تقریبی ایده آل
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

Let (A;E) be an exact category and F⊆Ext a subfunctor. A morphism φ in A is an F-phantom if the pullback of an E-conflation along φ 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 F⊆Ext 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,I⊥) 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(Λ-mod) of the category Λ-mod of finitely generated representations of an Artin algebra is complete.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 244, 10 September 2013, Pages 750-790
نویسندگان
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