Beyond totally reflexive modules and back: a survey on Gorenstein dimensions
LW Christensen, HB Foxby, H Holm - Commutative Algebra: Noetherian …, 2011 - Springer
Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …
homological dimensions for modules over commutative rings. The account includes the …
Frobenius pairs in abelian categories: Correspondences with cotorsion pairs, exact model categories, and Auslander–Buchweitz contexts
Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …
cotorsion pairs and model category structures. From the notion of relative generators, we …
FPn-Injective, FPn-Flat Covers and Preenvelopes, and Gorenstein AC-Flat Covers
D Bravo, S Estrada, A Iacob - Algebra Colloquium, 2018 - World Scientific
We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …
are both covering and preenveloping over any ring R. This includes the case of FP∞ …
[HTML][HTML] Duality pairs and stable module categories
J Gillespie - Journal of Pure and Applied Algebra, 2019 - Elsevier
Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …
Tilting complexes and codimension functions over commutative noetherian rings
M Hrbek, T Nakamura, J Šťovíček - Nagoya Mathematical Journal, 2024 - cambridge.org
In the derived category of a commutative noetherian ring, we explicitly construct a silting
object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” …
object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” …
Duality pairs, generalized Gorenstein modules, and Ding injective envelopes
J Gillespie, A Iacob - Comptes …, 2022 - comptes-rendus.academie-sciences …
Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …
Most examples satisfy further properties making them what we call semi-complete duality …
Relative Gorenstein flat modules and dimension
In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …
survey of their behavior in terms of both structural and dimension properties. We relate the …
Duality pairs and FP-injective modules over formal triangular matrix rings
L Mao - Communications in Algebra, 2020 - Taylor & Francis
Abstract Suppose that T=(A 0 UB) is a formal triangular matrix ring, where A and B are rings
and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using …
and U is a (B, A)-bimodule. We first study how to construct duality pairs of T-modules using …
Duality pairs, phantom maps, and definability in triangulated categories
I Bird, J Williamson - arXiv preprint arXiv:2202.08113, 2022 - arxiv.org
We define duality triples and duality pairs in compactly generated triangulated categories
and investigate their properties. This enables us to give an elementary way to determine …
and investigate their properties. This enables us to give an elementary way to determine …
Gorenstein injective covers and envelopes over noetherian rings
E Enochs, A Iacob - Proceedings of the American Mathematical Society, 2015 - ams.org
Gorenstein injective covers and envelopes over noetherian rings Page 1 PROCEEDINGS OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 1, January 2015, Pages …
THE AMERICAN MATHEMATICAL SOCIETY Volume 143, Number 1, January 2015, Pages …