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 …
Using semidualizing complexes to detect Gorenstein rings
S Sather-Wagstaff, J Totushek - Archiv der Mathematik, 2015 - Springer
A result of Foxby states that if there exists a complex with finite depth, finite flat dimension,
and finite injective dimension over a local ring R, then R is Gorenstein. In this paper we …
and finite injective dimension over a local ring R, then R is Gorenstein. In this paper we …
Homological aspects of semidualizing modules
R Takahashi, D White - Mathematica Scandinavica, 2010 - JSTOR
We investigate the notion of the C-projective dimension of a module, where C is a
semidualizing module. When C= R, this recovers the standard projective dimension. We …
semidualizing module. When C= R, this recovers the standard projective dimension. We …
Gorenstein homological dimension with respect to a semidualizing module and a generalization of a theorem of Bass
Let C be a semidualizing module for a commutative ring R. In this paper, we study the
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …
resulting modules of finite GC-projective dimension in Bass class, showing that they admit …
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 …
Semidualizing bimodules and related Gorenstein homological dimensions
A Xu, N Ding - Journal of Algebra and Its Applications, 2016 - World Scientific
Let SCR be a semidualizing bimodule with S left coherent and R right coherent. For a non-
negative integer n, it is shown that l. FP-id S (C)= r. FP-id R (C)≤ n if and only if every finitely …
negative integer n, it is shown that l. FP-id S (C)= r. FP-id R (C)≤ n if and only if every finitely …
[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 …
[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 …
Finitistic dimension and orthogonal classes of Gorenstein projective modules with respect to a semidualizing module
E Tavasoli - Communications in Algebra, 2019 - Taylor & Francis
Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is proved
that FPD (R)= sup {GPC− pd R (M)| M∈ BC (R) and GPC− pd R (M)<∞}, which is a …
that FPD (R)= sup {GPC− pd R (M)| M∈ BC (R) and GPC− pd R (M)<∞}, which is a …
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 …