Model structures and relative Gorenstein flat modules and chain complexes
S Estrada, A Iacob, MA Pérez - Categorical, homological and …, 2020 - books.google.com
A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …
structure on the category of left R-modules, for any associative ring R with identity, whose …
Gorenstein model structures and generalized derived categories
J Gillespie, M Hovey - Proceedings of the Edinburgh Mathematical …, 2010 - cambridge.org
In a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …
[HTML][HTML] The flat stable module category of a coherent ring
J Gillespie - Journal of Pure and Applied Algebra, 2017 - Elsevier
Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …
Relative Gorenstein flat modules and Foxby classes and their model structures
A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …
category, and if the model structure is abelian and hereditary, its homotopy category is …
Gorenstein flat representations of left rooted quivers
Z Di, S Estrada, L Liang, S Odabaşı - Journal of Algebra, 2021 - Elsevier
We study Gorenstein flat objects in the category Rep (Q, R) of representations of a left rooted
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …
Homotopy categories of totally acyclic complexes with applications to the flat-cotorsion theory
LW Christensen, S Estrada… - … combinatorial methods in …, 2020 - books.google.com
We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …
Gorenstein AC-projective complexes
J Gillespie - Journal of Homotopy and Related Structures, 2018 - Springer
Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …
Absolutely clean, level, and Gorenstein AC-injective complexes
D Bravo, J Gillespie - Communications in Algebra, 2016 - Taylor & Francis
Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …
homological algebra can be extended to an arbitrary ring R. This led to the notion of …
Stability of Gorenstein flat categories
G Yang, Z Liu - Glasgow Mathematical Journal, 2012 - cambridge.org
A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …
Singular compactness and definability for -cotorsion and Gorenstein modules
J Šaroch, J Št'ovíček - Selecta Mathematica, 2020 - Springer
We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …