[PDF][PDF] Homological Dimensions under Foxby Equivalence
YN Li, Z Huang - maths.nju.edu.cn
Let R and S be rings and RCS a semidualizing bimodule, and let T be a subcategory of the
Auslander class AC (S) and H={C⊗ ST| T∈ T}. Then for any left R-module M, the T …
Auslander class AC (S) and H={C⊗ ST| T∈ T}. Then for any left R-module M, the T …
Homological dimensions with respect to a semidualizing complex
J Totushek - 2015 - search.proquest.com
A fintitely generated R-module C is semidualizing if R= HomR (C, C) and [special charactes
omitted](C, C)= 0. In this dissertation we build off of Takahashi and White's P C-projective …
omitted](C, C)= 0. In this dissertation we build off of Takahashi and White's P C-projective …
[PDF][PDF] Homological invariants related to semidualizing bimodules
X Tang, Z Huang - Colloquium Mathematicum, 2019 - researchgate.net
Let R and S be rings and RCS a semidualizing bimodule. We show that the supremum of the
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …
Homological dimensions in cotorsion pairs
LA Hügel, OM Hernández - Illinois Journal of Mathematics, 2009 - projecteuclid.org
Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …
The homological dimensions of simple modules
N Ding, J Chen - Bulletin of the Australian Mathematical Society, 1993 - cambridge.org
We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …
Homological dimensions relative to preresolving subcategories II
Z Huang - Forum Mathematicum, 2022 - degruyter.com
Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …
[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 …
Global dimension and left derived functors of Hom
L Mao, N Ding - Science in China Series A: Mathematics, 2007 - Springer
It is well known that the right global dimension of a ring R is usually computed by the right
derived functors of Hom and the left projective resolutions of right R-modules. In this paper …
derived functors of Hom and the left projective resolutions of right R-modules. In this paper …
Gorenstein projective dimension relative to a semidualizing bimodule
Z Liu, Z Huang, A Xu - Communications in Algebra, 2013 - Taylor & Francis
Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …
Restricted Homological Dimensions of Complexes
D Wu, F Kong - Mathematical Notes, 2018 - Springer
We define and study the notions of restricted Tor-dimension and Ext-dimension for
unbounded complexes of left modules over associative rings. We show that, for a right …
unbounded complexes of left modules over associative rings. We show that, for a right …