… cycles of acyclic complexes of projectives (… Gorenstein rings, or more generally whether or
not it is possible to characterize Gorenstein rings in terms of acyclic complexes of (Gorenstein) …

… We also prove the following characterization of Gorenstein rings. Let R be a … acyclic complex
of injective modules, I, using the result for its (j − n)th cycle, we observe that ZjI is Gorenstein …

… We prove that a scheme is Gorenstein if and only if every acyclic complex of flat quasi-…
rings. This connection to singularity theory is our motivation for studying totally acyclic complexes …

… homotopy category of complexes of projective modules over a Noetherian ring. Truncation
… from the totally acyclic complexes to the singularity category. We show that if the ring is either …

… exact complex of injective modules a totally acyclic one? It is known, for example, that over a
commutative Noetherian ring of … In this section, we will define Iwanaga-Gorenstein rings and …

… over an associative ring. Among the applications, we give some new characterizations of …
–Gorenstein rings. In particular, we show that an associative ring R is Iwanaga–Gorenstein if …

… of an acyclic complex has Gorenstein versions in Gorenstein homological algebra. A cochain
… GI, the class of Gorenstein-injective modules, we will say that X is a GIacyclic complex. The …

… Gorenstein rings agrees with that of GROTI-IENDIECK whenever the latter is available. Next
we discuss more explicitly in w the behavior of Gorenstein rings … of M is an acyclic complex …

… has finite projective dimension if and only if R is Gorenstein, one … R is Gorenstein if and
only if every acyclic complex of projectives is totally acyclic, if and only if every acyclic complex of …

… is noetherian, then for each R-module M we can construct a not necessarily acyclic complex
… noetherian Gorenstein rings of dimension at most n are precisely the noetherian rings for …