The cotorsion pair generated by the Gorenstein projective modules and -pure-injective modules
M Cortés-Izurdiaga, J Šaroch - arXiv preprint arXiv:2104.08602, 2021 - arxiv.org
We prove that, if $\textrm {GProj} $ is the class of all Gorenstein projective modules over a
ring $ R $, then $\mathfrak {GP}=(\textrm {GProj},\textrm {GProj}^\perp) $ is a cotorsion pair …
ring $ R $, then $\mathfrak {GP}=(\textrm {GProj},\textrm {GProj}^\perp) $ is a cotorsion pair …
[PDF][PDF] Module classes induced by complexes and λ-pure-injective modules
M Cortés-Izurdiaga, J Šaroch - arXiv preprint arXiv:2104.08602, 2021 - researchgate.net
We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …
Resolutions as directed colimits
L Positselski - arXiv preprint arXiv:2312.07197, 2023 - arxiv.org
A general principle suggests that" anything flat is a directed colimit of countably presentable
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …
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 …
Complete cotorsion pairs in the category of complexes
Z Wang, Z Liu - Turkish Journal of Mathematics, 2013 - journals.tubitak.gov.tr
In this paper, we study completeness of cotorsion pairs in the category of complexes of R-
modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair …
modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair …
The orthogonal complement relative to the functor extension of the class of all Gorenstein projective modules
M Tamekkante - 2010 - projecteuclid.org
In this paper, we study the pair (GP(R),GP(R)^⊥) where GP(R) is the class of all Gorenstein
projective modules. We prove that it is a complete hereditary cotorsion theory, provided …
projective modules. We prove that it is a complete hereditary cotorsion theory, provided …
Generalized Gorenstein modules
A Iacob - Algebra Colloquium, 2022 - World Scientific
We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …
Gorenstein complexes and recollements from cotorsion pairs
J Gillespie - arXiv preprint arXiv:1210.0196, 2012 - arxiv.org
We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
The Right Orthogonal Class $\GP (R)^{\perp} $ via $\Ext$
M Tamekkante - arXiv preprint arXiv:0911.1272, 2009 - arxiv.org
In this paper, we study the pair $(\GP (R),\GP (R)^{\perp}) $ where $\GP (R) $ is the class of
all Gorenstein projective modules. We prove that it is complete hereditary cotorsion theory …
all Gorenstein projective modules. We prove that it is complete hereditary cotorsion theory …
Auslander conditions and tilting-like cotorsion pairs
J Wang, Y Li, J Wu, J Hu - Journal of Algebra, 2023 - Elsevier
We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …