Gorenstein FP-Injective Dimension for Complexes

J Hu, Y Geng, Z Xie, D Zhang - Communications in Algebra, 2015 - Taylor & Francis
This article is a continuous work of, where the coauthors introduced the notion of 𝒢-FP-
injective R-modules. In this article, we define a notion of 𝒢-FP-injective dimension for …

Triangle equivalences involving Gorenstein FP-injective modules

Z Di, X Zhang, Z Liu - Communications in Algebra, 2018 - Taylor & Francis
Recently, Hu et al. introduced the notion of Gorenstein FP-injective modules and
investigated a notion of Gorenstein FP-injective dimension for complexes. Let R be a left …

FP-injective dimensions and Gorenstein homology

G Yang, J Wang - Proceedings of the Edinburgh Mathematical …, 2022 - cambridge.org
Let $ R $ be a left coherent ring. It is proven that if an $ R $-module $ M $ has a finite FP-
injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the …

Homological invariants of unbounded complexes under Frobenius extensions

D Wu, Y Wang - Communications in Algebra, 2023 - Taylor & Francis
Abstract Let R⊂ S be a Frobenius extension of rings and M an S-complex. It is proven that if
the Gorenstein projective (injective) dimension of M as an S-complex is finite, then the …

On Gorenstein FP-Injective and Gorenstein Flat Complexes

D Xin, J Chen, X Zhang - Communications in Algebra, 2013 - Taylor & Francis
In this article, the concept of Gorenstein FP-injective modules and some related known
results are generalized to Gorenstein FP-injective complexes. Moreover, some new …

Homological dimensions of complexes related to cotorsion pairs

C Wei, L Wang, H Qiao - Turkish Journal of Mathematics, 2014 - journals.tubitak.gov.tr
Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B
dimension of unbounded complexes, which is given by means of dg-projective resolution …

Strongly Gorenstein flat and Gorenstein FP-injective modules

C Yang - Turkish Journal of Mathematics, 2013 - journals.tubitak.gov.tr
In this paper, we first study the properties of strongly Gorenstein flat (resp. Gorenstein FP-
injective) modules which are special Gorenstein projective (resp. Gorenstein injective) …

On Gorenstein flat dimension

S Bouchiba - Journal of Algebra and its Applications, 2015 - World Scientific
The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …

[HTML][HTML] Relative cohomology of complexes

Z Liu - Journal of Algebra, 2018 - Elsevier
Let R be an arbitrary ring and C a complex with finite Gorenstein projective dimension (that
is, the supremum of Gorenstein projective dimension of all R-modules in C is finite). For …

Coherent rings with finite self-FP-injective dimension

N Ding, J Chen - Communications in algebra, 1996 - Taylor & Francis
Coherent rings with finite self-FP-injective dimension Page 1 COMMUNICATIONS IN ALGEBRA,
24(9), 2963-2980 (1996) COHERENT RINGS WITH FINITE SELF-FP-INJECTIVE DIMENSION …