STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS
نویسندگان
چکیده
منابع مشابه
Infinite Dimensional Tilting Modules and Cotorsion Pairs
Classical tilting theory generalizes Morita theory of equivalence of module categories. The key property – existence of category equivalences between large full subcategories of the module categories – forces the representing tilting module to be finitely generated. However, some aspects of the classical theory can be extended to infinitely generated modules over arbitrary rings. In this paper,...
متن کاملTilting Cotorsion Pairs
Let R be a ring and T be a 1-tilting right R-module. Then T is of countable type. Moreover, T is of finite type in case R is a Prüfer domain.
متن کاملCotorsion pairs and model categories
The purpose of this paper is to describe a connection between model categories, a structure invented by algebraic topologists that allows one to introduce the ideas of homotopy theory to situations far removed from topological spaces, and cotorsion pairs, an algebraic notion that simultaneously generalizes the notion of projective and injective objects. In brief, a model category structure on a...
متن کاملRelative Cotorsion Modules and Relative Flat Modules
Let R be a ring, M a right R-module, and n a fixed non-negative integer. M is called n-cotorsion if Extn+1 R N M = 0 for any flat right R-module N . M is said to be n-flat if ExtR M N = 0 for any n-cotorsion right R-module N . We prove that ( n n is a complete hereditary cotorsion theory, where n (resp. n) denotes the class of all n-flat (resp. n-cotorsion) right R-modules. Several applications...
متن کاملCotorsion Pairs Induced by Duality Pairs
We introduce the notion of a duality pair and demonstrate how the left half of such a pair is “often” covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules—introduced by Enochs and Jenda—is covering when the ground ring has a dualizing complex.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2010
ISSN: 1015-8634
DOI: 10.4134/bkms.2010.47.5.1041