[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 …
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 …
Minimal complexes of cotorsion flat modules
P Thompson - arXiv preprint arXiv:1702.02985, 2017 - arxiv.org
Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …
modules to be minimal, in the sense that every self homotopy equivalence is an …
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 …
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 …
Homotopy categories of unbounded complexes of projective modules
Y Yoshino - Journal of the London Mathematical Society, 2022 - Wiley Online Library
We develop in this paper the stable theory for projective complexes, by which we mean to
consider a chain complex of finitely generated projective modules as an object of the factor …
consider a chain complex of finitely generated projective modules as an object of the factor …
[HTML][HTML] Gorenstein complexes and recollements from cotorsion pairs
J Gillespie - Advances in Mathematics, 2016 - Elsevier
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 …
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 injective precovers, covers, and envelopes
E Enochs, S Estrada, A Iacob - arXiv preprint arXiv:1301.5694, 2013 - arxiv.org
We give a sufficient condition for the class of Gorenstein injective modules be precovering: if
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …
The Nakayama functor and its completion for Gorenstein algebras
SB Iyengar, H Krause - arXiv preprint arXiv:2010.05676, 2020 - arxiv.org
Duality properties are studied for a Gorenstein algebra that is finite and projective over its
center. Using the homotopy category of injective modules, it is proved that there is a local …
center. Using the homotopy category of injective modules, it is proved that there is a local …