منابع مشابه
Cotorsion Theories and Splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is ExtR(G,G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more splitters, in fact we are able to prescribe the...
متن کاملNotes on Cotorsion Theories and Model Categories
These are notes for two talks given by Mark Hovey at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. Because they are notes, they are a bit more chatty and a bit more likely to contain errors than a paper would be, so caveat lector. They are based on the papers [Hov02], [Gil04b], and [Gil04a], and concern the rel...
متن کاملCotorsion theories cogenerated by א1-free abelian groups
Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.
متن کاملOn Whitehead Precovers
It is proved undecidable in ZFC + GCH whether every Z-module has a {Z}-precover. Let F be a class of R-modules of the form C = {A : Ext(A,C) = 0 for all C ∈ C} for some class C. The first author and Jan Trlifaj proved [7] that a sufficient condition for every module M to have an F -precover is that there is a module B such that F = {B} (= {A : Ext(B,A) = 0}). In [8], generalizing a method used ...
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.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2002
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309150000122x