Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

Abstract Distinctive characteristics of Iwanaga–Gorenstein rings are typically understood
through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein …

It is well-known that the weak global dimension of a ring does not exceed its global
dimension. Christensen et al. obtained a corresponding result in Gorenstein setting for …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. We give support to the …

On rings with finite Gorenstein weak global dimension Page 1 Journal of Algebra and Its
Applications Vol. 22, No. 5 (2023) 2350111 (15 pages) c© World Scientific Publishing Company …

For any group $ G $, the Gorenstein homological dimension ${\rm Ghd} _RG $ is defined to
be the Gorenstein flat dimension of the coefficient ring $ R $, which is considered as an …

Let $ R $ be a ring with Gwgldim $(R)<\infty $. We obtain a triangle-equivalence $\mathrm
{K}(R\text {-}\mathrm {GProj})\simeq\mathrm {K}(R\text {-}\mathrm {GInj}) $ which restricts to a …

In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups
over a commutative ring of finite weak Gorenstein global dimension and provide good …

设W 是包含所有内射模的模类. 通过在任意结合环上引入模的覆盖W-Gorenstein 平坦维数,
刻画W-Gorenstein 平坦模类的投射可解性, 并证明了: 对任意 R 模M 和任意正整数n, 若模M …

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 …