Local, colocal, and antilocal properties of modules and complexes over commutative rings
L Positselski - Journal of Algebra, 2024 - Elsevier
… complete) cotorsion theory for modules or complexes of … flat complexes of flat contraadjusted
modules and acyclic … and complexes arise in connection with cotorsion pairs, and it …
modules and acyclic … and complexes arise in connection with cotorsion pairs, and it …
A refinement of Gorenstein flat dimension via the flat–cotorsion theory
… complex T of flat-cotorsion modules such that the complexes … R ( W , T ) are acyclic for every
flat-cotorsion R-module W. An R-… flat-cotorsion if there exists a totally acyclic complex T of flat-…
flat-cotorsion R-module W. An R-… flat-cotorsion if there exists a totally acyclic complex T of flat-…
Remarks on derived complete modules and complexes
L Positselski - Mathematische Nachrichten, 2023 - Wiley Online Library
… (also derived I-torsion) complexes of R-modules, which appear in the … We also consider
I-adically flat R-modules. … 2] under the name of “co-torsion abelian groups”; this approach was …
I-adically flat R-modules. … 2] under the name of “co-torsion abelian groups”; this approach was …
Homology theories for complexes based on flats
L Liang - Glasgow Mathematical Journal, 2021 - cambridge.org
… ◦ -module G is called Gorenstein flat if there exists a F-totally acyclic complex T of flat R … A
Tate flat resolution of an R … , and acyclic DG-cotorsion Rcomplexes are actually cotorsion R-…
Tate flat resolution of an R … , and acyclic DG-cotorsion Rcomplexes are actually cotorsion R-…
A generalization of the flat cotorsion theory
A Stanculescu - arXiv preprint arXiv:2307.11208, 2023 - arxiv.org
… to abelian categories of the flat cotorsion theory for modules over a ring. Using the … flat
cotorsion theory we present a flat totally acyclic cotorsion theory in categories of chain complexes …
cotorsion theory we present a flat totally acyclic cotorsion theory in categories of chain complexes …
New model structures and projective (injective) cotorsion pairs
A Xu - Journal of Algebra and Its Applications, 2023 - World Scientific
… theory on modules (or complexes) over a more general ring. For a generic ring R, It is known
that the canonical projective cotorsion … hereditary cotosion pair is the flat cotorsion pair (F, C)…
that the canonical projective cotorsion … hereditary cotosion pair is the flat cotorsion pair (F, C)…
[PDF][PDF] Constructing K-theory spectra from algebraic structures with a class of acyclic objects
M Sarazola - 2021 - ecommons.cornell.edu
… one cotorsion pair, together with a chosen class of acyclic … we construct a category of chain
complexes of sets, and use our … Enochs used them to prove the flat cover conjecture: namely, …
complexes of sets, and use our … Enochs used them to prove the flat cover conjecture: namely, …
Homological invariants of unbounded complexes under Frobenius extensions
D Wu, Y Wang - Communications in Algebra, 2023 - Taylor & Francis
… Avramov and Foxby [Citation4] outlined the theory of homological dimensions for complexes.
… is called Gorenstein flat-cotorsion if there exists a totally acyclic complex of flat-cotorsion R-…
… is called Gorenstein flat-cotorsion if there exists a totally acyclic complex of flat-cotorsion R-…
On K-absolutely pure complexes
I Emmanouil, I Kaperonis - Journal of Algebra, 2024 - Elsevier
… has found many applications in representation theory and … that a complex of left R-modules
F is K-flat if the complex of … We say that the cotorsion pair is complete if for any object A ∈ A …
F is K-flat if the complex of … We say that the cotorsion pair is complete if for any object A ∈ A …
Acyclic complexes of injectives and finitistic dimensions
L Shaul - arXiv preprint arXiv:2303.08756, 2023 - arxiv.org
… is to relate properties of acyclic complexes of injective modules … acyclic complex of flat
cotorsion A-modules such that Fn = 0 for n ≪ 0. Every acyclic bounded below complex of cotorsion …
cotorsion A-modules such that Fn = 0 for n ≪ 0. Every acyclic bounded below complex of cotorsion …