‎ The representation theory of groups is one of the most interesting examples of the
interaction between physics and pure mathematics‎,‎ where group rings play the main role‎.‎ …

Let $ G $ be a group and $ R $ be a ring. We define the Gorenstein homological dimension
of $ G $ over $ R $, denoted by ${\rm Ghd} _ {R} G $, as the Gorenstein flat dimension of …

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 commutative ring, Γ be a group, and Γ′ be a subgroup of finite index. In this
paper, we study the class of Gorenstein flat (resp. Gorenstein cotorsion) modules over the …

Projectively coresolved Gorenstein flat modules were introduced by Saroch and Stovicek
and were shown to be Gorenstein projective. We give characterizations of Gorenstein …

Gorenstein homological algebra was introduced in categories of modules. But it has proved
to be a fruitful way to study various other categories such as categories of complexes and of …

We construct new complete cotorsion pairs in the categories of modules and chain
complexes over a Gorenstein ring $ R $, from the notions of Gorenstein homological …

Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13](however,
only a few nontrivial examples are known). Integral group rings over polycyclic-by-finite …

In this paper we develop the homological properties of the $(\mathcal {L},\mathcal {A}) $-
Gorenstein flat $ R $-modules $\mathcal {GF} _ {(\mathcal {F}(R),\mathcal {A})} $ proposed …

For any group G and any commutative ring R, the Gorenstein homological dimension
GhdRG, defined as the Gorenstein flat dimension of the trivial RG-module R, is …