Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory

LW Christensen, S Estrada… - … combinatorial methods in …, 2020 - books.google.com
totally acyclic complexes of flat-cotorsion A-modules, and thus to the stable category of
cotorsion Gorenstein flat … equivalent to the stable category of cotorsion Gorenstein flat A-modules. …

[HTML][HTML] Totally acyclic complexes

S Estrada, X Fu, A Iacob - Journal of Algebra, 2017 - Elsevier
… , algebraic topology and representation theory. Not only do these areas … flat module is a cycle
of an F-totally acyclic complex of flat … Then every strongly cotorsion module has Gorenstein …

Periodic modules and acyclic complexes

S Bazzoni, M Cortés-Izurdiaga, S Estrada - … and Representation Theory, 2020 - Springer
… every acyclic complex of cotorsion modules has cotorsioncomplex of cotorsion modules
and F is an acyclic complex of … between flat Proj-periodic modules and acyclic complexes of …

Totally Acyclic Complexes

HM Zolt - 2019 - digitalcommons.georgiasouthern …
… algebra, noncommutative algebra, representation theory, and model category theory [13].
That … cotorsion, making it cotorsion flat. This implies that B is an exact complex of cotorsion flat

On strongly flat and weakly cotorsion modules

L Positselski, A Slávik - Mathematische Zeitschrift, 2019 - Springer
… The aim of the theory developed in this paper is to describe flat modules over associative …
We denote this complex by and place it in the cohomological degrees 0 and 1 (so \(T^0=\…

Minimal complexes of cotorsion flat modules

P Thompson - arXiv preprint arXiv:1702.02985, 2017 - arxiv.org
… ], we show that minimal complexes of cotorsion flat R-modules … complexes of projective or
injective Rmodules, one of our goals is to show (Theorem 3.5) that a complex B of cotorsion flat

Acyclic complexes and Gorenstein rings

S Estrada, A Iacob, H Zolt - Algebra Colloquium, 2020 - World Scientific
… , as well as in representation theory and model category theory. This is the reason why the
… (2) Every exact complex of cotorsion-flat right R-modules is F-totally acyclic. (3) Every exact …

Purity and ascent for Gorenstein flat cotorsion modules

I Bird - arXiv preprint arXiv:2108.08135, 2021 - arxiv.org
… We will call a right (F∩C)(R)-totally acyclic complex a totally acyclic complex of flat-… A
refinement of Gorenstein flat dimension via the flat-cotorsion theory. J. Algebra, 567:346–370, 2021…

Gorenstein Homological Dimension of Groups Through Flat-Cotorsion Modules

A Hajizamani - Mathematics Interdisciplinary Research, 2024 - mir.kashanu.ac.ir
… in the theory of … totally acyclic complex of flat-cotorsion R-modules, then by symmetry,
all the kernels, cokernels and the images of the differentials of L are Gorenstein flat-cotorsion

Flat cotorsion modules over Noether algebras

R Kanda, T Nakamura - Documenta Mathematica, 2022 - ems.press
… role in homological algebra and representation theory (eg, [AB89], [… of totally acyclic
complexes of flat cotorsion modules is equivalent to the stable category of Gorenstein-flat cotorsion