There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

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 …

Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

In this paper, we study a particular case of Gorenstein projective, injective, and flat modules,
which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These …

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-
module M is called strongly Gorenstein flat if there is an exact sequence⋯→ P1→ P0→ P0→ …

An n-FC ring is a left and right coherent ring whose left and right self-FP-injective dimension
is n. The work of Ding and Chen shows that these rings possess properties which generalize …

For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

In this paper, we prove that the global Gorenstein projective dimension of a ring $ R $ is
equal to the global Gorenstein injective dimension of $ R $ and that the global Gorenstein …

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M
is called Gorenstein FP-injective if there is an exact sequence⋯→ E1→ E0→ E0→ E1→⋯ of …