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 …

We characterize a ring over which every left module of finite length has an injective hull of
finite length. Using this, we show that finite normalizing extensions of such a ring also have …

A ring R is called left “GF-closed”, if the class of all Gorenstein flat left R-modules is closed
under extensions. The class of left GF-closed rings includes strictly the one of right coherent …

Let R be a commutative noetherian henselian non-Gorenstein local ring of depth zero.
Denote by mod R the category of all finitely generated R-modules, and by the full …

Let R be a left coherent ring, S any ring and RωS an (R, S)-bimodule. Suppose ωS has an
ultimately closed FP-injective resolution and RωS satisfies the conditions:(1) ωS is finitely …

Barucci and Fröberg (1997)[2] introduced the notion of an almost Gorenstein ring in the case
of an analytically unramified local ring (R, m). In this work we provide a framework that …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

According to Auslander, a Noetherian ring R is called n-Gorenstein for n≥ 1 if in a minimal
injective resolution 0→ RR→ E0→ E1→…→ En→,…, the flat dimension of each Ei is at most …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

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