Relative projective and injective dimensions
D Bennis, JR García Rozas… - Communications in …, 2016 - Taylor & Francis
We study the concepts of the 𝒫 C-projective and the ℐ C-injective dimensions of a module in
the noncommutative case, weakening the condition of C being semidualizing. We give the …
the noncommutative case, weakening the condition of C being semidualizing. We give the …
Global dimensions of rings with respect to a semidualizing module
G Zhao, J Sun - arXiv preprint arXiv:1307.0628, 2013 - arxiv.org
In this paper, the notion of strongly G_C-projective and injective modules is introduced,
where C is a semidualizing module. Using these modules we can obtain a new …
where C is a semidualizing module. Using these modules we can obtain a new …
Gorenstein Analogue of Auslander's Theorem on the Global Dimension
D Bennis, K Hu, F Wang - Communications in Algebra, 2015 - Taylor & Francis
In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …
Relative Gorenstein dimensions
D Bennis, JR García Rozas, L Oyonarte - Mediterranean Journal of …, 2016 - Springer
In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …
have been subject of several works as interesting extensions of (Gorenstein) homological …
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] Gorenstein homological dimensions with respect to a semidualizing module
Z Zhang, J Wei - International Electronic Journal of Algebra, 2018 - dergipark.org.tr
In this paper, let R be a commutative ring and C a semidualizing module. We investigate the
(weak) C-Gorenstein global dimension of R and we get a simple formula to compute the C …
(weak) C-Gorenstein global dimension of R and we get a simple formula to compute the C …
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 …
On restricted injective dimensions of complexes
W Dejun, L Zhongkui - Communications in Algebra, 2013 - Taylor & Francis
Let R be a commutative Noetherian ring. If cmd R≤ 1, then it is shown that for any R-module
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …
the large restricted injective dimension is a refinement of the Gorenstein injective dimension …
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 …