Relative Gorenstein flat modules and dimension
In this article, the new concept of relative Gorenstein flat modules is introduced. We give a
survey of their behavior in terms of both structural and dimension properties. We relate the …
survey of their behavior in terms of both structural and dimension properties. We relate the …
Relative Gorenstein objects in abelian categories
Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …
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 …
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 …
[HTML][HTML] The role of w-tilting modules in relative Gorenstein (co) homology
Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …
Exact categories and infinite tilting
W Rump - Communications in Algebra, 2021 - Taylor & Francis
It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …
coherence property and the closure condition that exact sequences are acyclic. The …
Relative weak global Gorenstein dimension, AB-contexts and model structures
In this paper we introduce and study the weak Gorenstein global dimension of a ring $ R $
with respect to a left $ R $-module $ C $. We provide several characterizations of when this …
with respect to a left $ R $-module $ C $. We provide several characterizations of when this …
[HTML][HTML] Relative Gorenstein dimensions over triangular matrix rings
Let A and B be rings, U a (B, A)-bimodule, and T= A 0 UB the triangular matrix ring. In this
paper, several notions in relative Gorenstein algebra over a triangular matrix ring are …
paper, several notions in relative Gorenstein algebra over a triangular matrix ring are …
Relative Gorenstein global dimension
D Bennis, JR Garcia Rozas… - International Journal of …, 2016 - World Scientific
We study the relative Gorenstein projective global dimension of a ring with respect to a
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …
weakly Wakamatsu tilting module C. We prove that this relative global dimension is finite if …
Foxby equivalence relative to -weak injective and -weak flat modules
Z Gao, T Zhao - arXiv preprint arXiv:1706.00568, 2017 - arxiv.org
Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …