Homological dimension based on a class of Gorenstein modules and recollement situations

W Chen - projecteuclid.org
… We use pdR, idR, and fdR to stand for projective, injective, and flat dimension respectively…
weak global dimension of a ring T. By [8], we know that the Gorenstein weak global dimension

Strongly (T, n)-Coherent Rings, (T, n)-Semihereditary Rings and (T, n)-Regular Rings

Z Zhu - Czechoslovak Mathematical Journal, 2020 - Springer
… n-FP-injective modules and weakly n-flat modules in [15]. Fol… We recall: A subclass T of left
R-modules is called a weak … Let R be a non-coherent commutative ring of weak dimension

On FI-cotorsion modules and dimensions

AD Alqahtani, K Ouarghi - J. Math. Comput. Sci., 2021 - scik.org
… We prove that every cotorsion flat R-module is FI-cotorsion and we … of finite weak dimension.
From [4, Lemma 5.3.27] and for any flat cotorsion R-module F there exists injective modules

On the monoidal invariance of the cohomological dimension of Hopf algebras

J Bichon - Comptes Rendus. Mathématique, 2022 - numdam.org
… and both have finite cohomological dimension, then cd(A) = … , since finite-dimensional Hopf
algebras are self-injective, we … connects Question 1 to a weak form of an important historical …

Frobenius functors and Gorenstein flat dimensions

J Hu, H Li, Y Geng, D Zhang - Communications in Algebra, 2020 - Taylor & Francis
homological properties, such as the Gorenstein projective … of R is equal to the left weak
Gorenstein global dimension of S … ) = 0 for all i ≥ 1 and injective R op -modules E. Proceed in this …

Duality pairs, generalized Gorenstein modules, and Ding injective envelopes

J Gillespie, A Iacob - Comptes …, 2022 - comptes-rendus.academie-sciences …
… We attach a relative theory of Gorenstein homological … the homological theory of the AC-Gorenstein
modules defined … of all flat Rmodules and I to be the class of all injective R◦-modules. …

An alternative perspective on pure-projectivity of modules

Y Alagöz, Y Durg̃un - São Paulo Journal of Mathematical Sciences, 2020 - Springer
… and modules, including FP-injective and FP-projective modules… 4 of this paper, psp-poor
modules studied and investigated … In particular, projective dimension of every flat module is less …

On characterizations of w-coherent rings II

X Zhang, F Wang - Communications in Algebra, 2021 - Taylor & Francis
… E w -stationary modules over all injective modules E and show … the homological properties
of w-strictly stationary modules … rings, domains of Krull dimension ≤ 1 and so on. A maximal …

Weak holonomicity for equivariant modules on rigid analytic flag varieties

TMP Vu - arXiv preprint arXiv:2011.10019, 2020 - arxiv.org
… the homological grade of a module as its codimension. This is based on the key fact that …
with A Gorenstein (ie A is of finite self-injective dimension), then U(L) is Auslander-Gorenstein of …

Some characterizations of coherent rings in terms of strongly FP-injective modules

M Chen, H Kim, F Wang, X Zhang - Communications in Algebra, 2020 - Taylor & Francis
… FP-injective module of injective dimension 1 may not be … if and only if any weak injective
R-module is FP-injective [Citation9, … FP-injective R-module if and only if M + is a flat R-module. …