How To Make Ext Vanish

@article{Eklof2001HowTM,
  title={How To Make Ext Vanish},
  author={Paul C. Eklof and Jan Trlifaj},
  journal={Bulletin of the London Mathematical Society},
  year={2001},
  volume={33}
}
  • P. Eklof, J. Trlifaj
  • Published 1 January 2001
  • Mathematics
  • Bulletin of the London Mathematical Society
We describe a general construction of a module A from a given module B such that Ext(B, A) = 0, and we apply it to answer several questions on splitters, cotorsion theories and saturated rings. 
Continuous limits of tilting modules
TLDR
A constructive argument is provided to obtain an infinite generated tilting module from a family of  tilting modules satisfying some  hypotheses and the result is applied over a hereditary algebra to get the Lukas Tilting module.
Relative Nonhomogeneous Koszul Duality
All the constructions of Chapters 1-10 can be carried out with the category of k-modules replaced by the category of graded k-modules.
ON THE EXISTENCE OF FLAT COVERS IN R-gr
Recently, a proof of the existence of a flat cover of any module over an arbitrary associative ring with unit has been finally given (see 4-5). In this paper we prove the existence of flat covers in
FI -Injective Resolutions and Dimensions
In this paper, we show the existence of FI-injective preenvelopes over coherent rings, characterize FI-injective resolutions and define FIinjective dimension for modules and rings. It measures how
Bounded complexes of cotorsion sheaves
ABSTRACT We provide a necessary and sufficient condition which ensure that every flat quasi-coherent sheaf has finite cotorsion dimension. Also, we will show that every locally noetherian scheme with a
WHEN ARE PURE-INJECTIVE ENVELOPES OF FLAT MODULES FLAT?
ABSTRACT The question is answered in terms of flat covers, flat cotorsion modules, and cotorsion envelopes. It is shown that the corresponding class of rings properly contains that of coherent rings.
One Dimensional Tilting Modules are of Finite Type
We prove that every tilting module of projective dimension at most one is of finite type, namely that its associated tilting class is the Ext-orthogonal of a family of finitely presented modules of
A note on tilting sequences
We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
All Modules Have Gorenstein Flat Precovers
TLDR
It is shown in the paper that every R-module has a Gorenstein flat precover.
Cotorsion pairs and model structures on Ch(R)
Abstract We show that if the given cotorsion pair $(\mathcal{A},\mathcal{B})$ in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of
...
...

References

SHOWING 1-10 OF 35 REFERENCES
Flat covers of modules
Envelopes and covers.- Fundamental theorems.- Flat covers and cotorsion envelopes.- Flat covers over commutative rings.- Applications in commutative rings.
Injective and flat covers, envelopes and resolvents
Using the dual of a categorical definition of an injective envelope, injective covers can be defined. For a ringR, every leftR-module is shown to have an injective cover if and only ifR is left
Balanced subgroups of abelian groups
  • R. Hunter
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1975
The balanced subgroups of Fuchs are generalised to arbitrary abelian groups. Projectives and injectives with respect to general balanced exact sequences are classified; a new class of groups is
COTORSION THEORIES AND SPLITTERS
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext R(G; G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and
Homological Dimensions of Modules
Introduction Part I. Introductory ring and category theory: General definitions, notations, example Basic properties of projectives, injectives, flat modules, Hom and $\otimes$ Basic commutative
Cotilting and a Hierarchy of Almost Cotorsion Groups
We describe the structure of all cotilting and partial cotilting groups, and of all cotilting torsion-free classes of groups. Under V = L, we also describe all tilting and partial tilting groups. As
Almost free splitters
Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is Ext_R(G,G)=0 holds. For simplicity we will call such modules splitters. Our investigation continues
Whitehead test modules
A (right R-) module N is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module M , ExtR(M,N) = 0 implies M is projective. Dually, i-test modules are
Automorphismengesättigte Klassen Abzählbarer Abelscher Gruppen
Die vorliegende Arbeit beschaftigt sich mit der Untersuchung von Klassen K abelscher Gruppen, die den beiden folgenden Bedingungen genugen: (I) Abelsche Automorphismengruppen von K-Gruppen sind
Homological algebra and set theory
...
...