Relative Tor functors with respect to a semidualizing module
Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
Reflexivity and ring homomorphisms of finite flat dimension
A Frankild, S Sather-Wagstaff - Communications in Algebra®, 2007 - Taylor & Francis
In this article we present a systematic study of the reflexivity properties of homologically finite
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …
complexes with respect to semidualizing complexes in the setting of nonlocal rings. One …
Gorenstein projective, injective and flat modules over trivial ring extensions
L Mao - arXiv preprint arXiv:2305.15656, 2023 - arxiv.org
We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …
Homological dimensions relative to preresolving subcategories
Z Huang - 2014 - projecteuclid.org
We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …
abelian category and define homological dimensions and codimensions relative to these …
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 …
Semidualizing Modules over Numerical Semigroup Rings
E Celikbas, H Geller, T Kobayashi - arXiv preprint arXiv:2306.14989, 2023 - arxiv.org
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …
[HTML][HTML] Complete intersection dimensions and Foxby classes
S Sather-Wagstaff - Journal of Pure and Applied Algebra, 2008 - Elsevier
Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …
Presentations of rings with non-trivial semidualizing modules
DA Jorgensen, GJ Leuschke… - Collectanea mathematica, 2012 - Springer
Let R be a commutative noetherian local ring. A finitely generated R-module C is
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
semidualizing if it is self-orthogonal and\rm Hom _R (C, C) ≅ R. We prove that a Cohen …
Gorenstein cohomology in abelian categories
S Sather-Wagstaff, T Sharif, D White - Journal of Mathematics of …, 2008 - projecteuclid.org
We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …
Modules of finite homological dimension with respect to a semidualizing module
S Sather-Wagstaff, S Yassemi - Archiv der Mathematik, 2009 - Springer
Modules of finite homological dimension with respect to a semidualizing module Page 1
Arch. Math. 93 (2009), 111–121 c© 2009 Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020111-11 …
Arch. Math. 93 (2009), 111–121 c© 2009 Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020111-11 …