We consider the following question: when is every exact complex of injective modules a
totally acyclic one? It is known, for example, that over a commutative Noetherian ring of finite …

It is known that over an Iwanaga–Gorenstein ring the Gorenstein injective (Gorenstein
projective, Gorenstein flat) modules are simply the cycles of acyclic complexes of injective …

We prove first (Proposition 3) that, over any ring R, an acyclic complex of projective modules
is totally acyclic if and only if the cycles of every acyclic complex of Gorenstein projective …

Let R be a noetherian commutative ring, anda complex of flat R-modules. We prove that if is
acyclic for every ρ ϵ Spec R, then is acyclic, and H0 () is R-flat. It follows that if is a (possibly …

For a given class of modules A, let A˜ be the class of exact complexes having all cycles in A,
and dw (A) the class of complexes with all components in A. Denote by GI the class of …

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every
acyclic complex of injective modules is totally acyclic. We extend this characterization, which …

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every
acyclic complex of injective modules is totally acyclic. We extend this characterization, which …

This paper studies infinite acyclic complexes of finitely generated free modules over a
commutative noetherian local ring $(R,\fm) $ with $\fm^ 3= 0$. Conclusive results are …

In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of
finitely generated free modules over a commutative local ring which share a common syzygy …

We prove that every∑-pure-injective module over a serial ring is serial and every∑-pure-
injective faithful indecomposable module over a serial ring is∑-injective. Moreover, every …