We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

We study the Gorenstein weak global dimension of associative rings and its relation to the
Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

Projectively coresolved Gorenstein flat modules were introduced recently by Saroch and
Stovicek and were shown to be Gorenstein projective. While the relation between …

We give necessary and sufficient conditions in order for the class of projectively coresolved
Gorenstein flat modules, PGF (respectively that of projectively coresolved Gorenstein B flat …

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 …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

The Gorenstein cohomological dimension of a group G generalizes the ordinary
cohomological dimension of G, in the sense that the two invariants coincide when the latter …

In this paper, we introduce and study the projectively coresolved Gorenstein flat dimension
of a group G over a commutative ring R and we prove that this dimension enjoys all the …

In this short article, we will be principally investigating two classes of modules over any
given group ring–the class of Gorenstein projectives and the class of Benson's cofibrants …