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 …
Homological invariants associated to semi-dualizing bimodules
T Araya, R Takahashi, Y Yoshino - Journal of Mathematics of …, 2005 - projecteuclid.org
Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …
Gerko. That is a homological invariant sharing many properties with projective dimension …
[PDF][PDF] Complete intersection dimension
LL Avramov, VN Gasharov, IV Peeva - Publications Mathématiques de …, 1997 - numdam.org
A new homological invariant is introduced for a finite module over a commutative noetherian
ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained …
ring: its CI-dimension. In the local case, sharp quantitative and structural data are obtained …
[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 …
FP-PROJECTIVE DIMENSIONS
L Mao, N Ding - Communications in Algebra®, 2005 - Taylor & Francis
We define a dimension, called an FP-projective dimension, for modules and rings. It
measures how far away a finitely generated module is from being finitely presented, and …
measures how far away a finitely generated module is from being finitely presented, and …
On finite weak and injective dimension
LG Chouinard - Proceedings of the American Mathematical Society, 1976 - ams.org
An extension is given of the theorem relating projective dimension to depth for a finitely
generated module of finite projective dimension over a commutative Noetherian local ring …
generated module of finite projective dimension over a commutative Noetherian local ring …
Copure injective modules
EE Enochs, OMG Jenda - Quaestiones Mathematicae, 1991 - Taylor & Francis
A module is said to be copure injective if it is injective with respect to all modules A⊂ B with
B/A injective. We first characterize submodules that have the extension property with respect …
B/A injective. We first characterize submodules that have the extension property with respect …
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 …
The finitistic dimension conjecture and relatively projective modules
C Xi, D Xu - Communications in Contemporary Mathematics, 2013 - World Scientific
The famous finitistic dimension conjecture says that every finite-dimensional 𝕂-algebra over
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …
a field 𝕂 should have finite finitistic dimension. This conjecture is equivalent to the following …
Construction of modules with finite homological dimensions
O Veliche - Journal of Algebra, 2002 - Elsevier
A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …