Results 21 to 30 of about 10,608 (98)

Vanishing of cohomology over Cohen--Macaulay rings [PDF]

, 2012
A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings - colloquially called AC rings - that satisfy a natural condition on vanishing of cohomology.
Christensen, Lars Winther, Holm, Henrik
core   +1 more source

Gorenstein dimension over some rings of the form R [0 plus]C [PDF]

, 2014
Given a semidualizing module C over a commutative Noetherian ring, Holm and Jorgensen [Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl.
Pye Phyo Aung
semanticscholar   +1 more source

Homological dimensions for co-rank one idempotent subalgebras [PDF]

, 2015
Let $k$ be an algebraically closed field and $A$ be a (left and right) Noetherian associative $k$-algebra. Assume further that $A$ is either positively graded or semiperfect (this includes the class of finite dimensional $k$-algebras, and $k$-algebras ...
Ingalls, Colin, Paquette, Charles
core   +1 more source

The twisted inverse image pseudofunctor over commutative DG rings and perfect base change

, 2017
Let $K$ be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings $A$ over $K$, such that $H^0(A)$ is essentially of finite type over $K$, and $A$ has finite ...
Shaul, Liran
core   +1 more source

Homological properties of the relative Frobenius morphism [PDF]

This work concerns maps of commutative noetherian local rings containing a field of positive characteristic. Given such a map $\varphi$ of finite flat dimension, the results relate homological properties of the relative Frobenius of $\varphi$ to those of
Peter Mcdonald
semanticscholar   +1 more source

Gorenstein Global Dimensions and Cotorsion Dimension of Rings [PDF]

, 2007
In this article, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this
Driss Bennis, N. Mahdou
semanticscholar   +1 more source

Some homological criteria for regular, complete intersection and Gorenstein rings [PDF]

, 2013
Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field (Serre, Avramov, Auslander). It is also known that in positive characteristic,
Majadas, Javier
core  

Gorenstein projective and injective dimensions over Frobenius extensions

, 2018
Let $R\subset A$ be a Frobenius extension of rings. We prove that: (1) for any left $A$-module $M$, $_{A}M$ is Gorenstein projective (injective) if and only if the underlying left $R$-module $_{R}M$ is Gorenstein projective (injective). (2) if $\mathrm{G}
Ren, Wei
core   +1 more source

The equicharacteristic case of some homological conjectures on local rings

, 1974
This is an announcement of proofs of the intersection conjecture of Peskine and Szpiro and, hence, also, of M. Auslander's zerodivisor conjecture and of an affirmative answer to Bass' question for any equicharacteristic local ring R.
M. Hochster
semanticscholar   +1 more source

Super finitely presented modules and Gorenstein projective modules

, 2015
Let $R$ be a commutative ring. An $R$-module $M$ is said to be super finitely presented if there is an exact sequence of $R$-modules $\cdots\rightarrow P_n\rightarrow\cdots \rightarrow P_1\rightarrow P_0\rightarrow M\rightarrow 0$ where each $P_i$ is ...
Kim, Hwankoo, Qiao, Lei, Wang, Fanggui
core   +1 more source