This chapter discusses the homological theory of modules over Gorenstein rings. A
characteristic feature is the decomposition of the module category into two orthogonal …

We study three triangulated categories associated to a Gorenstein ring, that is, a right-and
left-noetherian ring with finite right and left injective dimension. After a survey of exact …

We study approximations of modules of finite Gorenstein flat dimension by (projectively
coresolved) Gorenstein flat modules and modules of finite flat dimension. These …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …

Let $\Lambda $ be an arbitrary monomial algebra. We investigate the stable category
$\underline {\operatorname {Gproj}}^{\mathbb {Z}}\Lambda $ of graded Gorenstein …

Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

arXiv:math/9809121v2 [math.AC] 31 Mar 1999 Page 1 arXiv:math/9809121v2 [math.AC] 31 Mar
1999 GORENSTEIN DIMENSION OF MODULES VLADIMIR MASEK Contents 0. Introduction 1 …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …