Corpus ID: 226979798

An explicit self-dual construction of complete cotorsion pairs in the relative context

@article{Positselski2020AnES,
  title={An explicit self-dual construction of complete cotorsion pairs in the relative context},
  author={L. Positselski},
  journal={arXiv: Rings and Algebras},
  year={2020}
}
Let $R\to A$ be a homomorphism of associative rings, and let $(\mathcal F,\mathcal C)$ be a hereditary complete cotorsion pair in $R\mathsf{-Mod}$. Let $(\mathcal F_A,\mathcal C_A)$ be the cotorsion pair in $A\mathsf{-Mod}$ in which $\mathcal F_A$ is the class of all left $A$-modules whose underlying $R$-modules belong to $\mathcal F$. Assuming that the $\mathcal F$-resolution dimension of every left $R$-module is finite and the class $\mathcal F$ is preserved by the coinduction functor… Expand

References

SHOWING 1-10 OF 44 REFERENCES
Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre–Grothendieck duality
For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category ofExpand
The Homological Theory of Maximal Cohen-Macaulay Approximations
Soclete Mathematlque de FranceMemoire n° 38, 1989, p.5-37.THE HOMOLOGICAL THEORYOFMAXIMAL COHEN-MACAULAY APPROXIMATIONSbyMaurice Auslander (Brandeis) and Ragnar-Olaf Buchweitz (Toronto)Summary. Let RExpand
Finitistic dimension and a homological generalization of semi-primary rings
Introduction. If P is a ring and M a left P-module, then homological algebra attaches three dimensions to M, projective, weak, and injective(1)By taking the supremum of one of these dimensions as MExpand
Flat covers and flat cotorsion modules
It is not known whether modules over an arbitrary ring have flat covers, however for certain modules over commutative noetherian rings they can be shown to exist. These covers, in turn, have anExpand
Approximations and Endomorphism Algebras of Modules
The category of all modules over a general associative ring is too complex to admit any reasonable classification. Thus, unless the ring is of finite representation type, one must limit attempts atExpand
Colocalization and cotilting for commutative noetherian rings
Abstract For a commutative noetherian ring R , we investigate relations between tilting and cotilting modules in Mod – R and Mod – R m , where m runs over the maximal spectrum of R . For each n ω ,Expand
On the existence of precovers
It is proved consistent with ZFC +GCH that for every Whitehead group A of infinite rank, there is a Whitehead group HA such that Ext(HA, A) 6= 0. This is a strong generalization of the consistency ofExpand
Test sets for factorization properties of modules
TLDR
The notion of a cotorsion pair is used to study generalizations and dualizations of factorization properties in dependence on the algebraic structure of the underlying ring $R$ and on additional set-theoretic hypotheses. Expand
Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
This paper can be thought of as an extended introduction to arXiv:0708.3398; nevertheless, most of its results are not covered by loc. cit. We consider the derived categories of DG-modules,Expand
Pseudo-dualizing complexes and pseudo-derived categories
The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothetyExpand
...
1
2
3
4
5
...