Rings of invariants can have nice homological properties even if they do not have finite
global dimension. Watanabe's Theorem [W] gives conditions when the fixed subring of a …

Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be
Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A …

The object of this note is to study commutative noetherian n-Gorenstein rings. The first result
is: if each module satisfying Samuel's conditions $({{\text {a}} _i}) $ for some $ i\leqq n $ is an …

One new trend in commutative ring theory, pioneered in [2-4], is to look at homological
properties of homomorphisms of rings, rather than settling for homological properties of …

Commutative noetherian Gorenstein rings (ie, rings of finite selfinjective dimension) were
first studied by Bass in 1963 [2]. S is a Gorenstein ring of injective dimension one if and only …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

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 …

Auslander introduced the notion of k-Gorenstein rings in the late sixties, as a non-
commutative version of Bass's commutative Gorenstein rings. The class of k-Gorenstein …

It was proved by Beligiannis and Krause that over certain Artin algebras, there are
Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective …

The main result asserts that a local commutative Noetherian ring is Gorenstein, if it
possesses a non-zero cyclic module of finite Gorenstein injective dimension. From this …