کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4667653 1345471 2007 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The phantom cover of a module
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
The phantom cover of a module
چکیده انگلیسی

A morphism of left R-modules is a phantom morphism if for any morphism , with A finitely presented, the composition fg factors through a projective module. Equivalently, Tor1(X,f)=0 for every right R-module X. It is proved that every R-module possesses a phantom cover, whose kernel is pure injective.If is the category of finitely presented right R-modules modulo projectives, then the association M↦Tor1(−,M) is a functor from the category of left R-modules to that of the flat functors on . The phantom cover is used to characterize when this functor is faithful or full. It is faithful if and only if the flat cover of every module has a pure injective kernel; this is equivalent to the flat cover being the phantom cover. The question of fullness is only reasonable when the functor is restricted to the subcategory of cotorsion modules. This restriction is full if and only if every phantom cover of a cotorsion module is pure injective.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 215, Issue 1, 20 October 2007, Pages 220-249