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Yuji Yoshino

Publications and source records attributed to Yuji Yoshino.

29 records · Page 2Linked to original sources
arXiv2010

Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring $R[x,f]$ that are Artinian as $R$-modules and the category of right $R[x,f]$-modules that are Noetherian as $R$-modules.

math.AC↗
arXiv2010

On the existence of embeddings into modules of finite homological dimensions

Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.

math.AC↗
arXiv2010

Abstract local cohomology functors

We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor associated with a given pair of ideals are characterized as elements of the set of all the abstract local cohomology functors.

math.AC↗
arXiv2008

Local cohomology based on a nonclosed support defined by a pair of ideals

We introduce an idea for generalization of a local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study their various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with the ordinary local cohomology.

math.AC↗
arXiv2007

On Ext-indices of ring extensions

In this paper we are concerned with the finiteness property of Ext-indices of several ring extensions. In this direction, we introduce some conjectures and discuss the relationship of them. Also we give affirmative answers to these conjectures in some special cases. Furthermore, we prove that the trivial extension of an Artinian local ring by its residue class field is always of finite Ext-index and we show that the Auslander-Reiten conjecture is true for this type of rings.

math.AC↗
arXiv2007

Mutation in triangulated categories and rigid Cohen-Macaulay modules

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

math.RT↗
arXiv2005

Homological invariants associated to semi-dualizing bimodules

Cohen-Macaulay dimension for modules over a commutative noetherian local ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension. The main purpose of this paper is to extend the notion of Cohen-Macaulay dimension for modules over commutative noetherian local rings to that for bounded complexes over non-commutative noetherian rings.

math.AC↗
arXiv2004

A functorial approach to modules of G-dimension zero

Let $R$ be a commutative Noetherian ring and let $\G$ be the category of modules of G-dimension zero over $R$. We denote the associated stable category by $\pG$. We show that the functor category $\modpG$ is a Frobenius category and we argue how this property could characterize $\G$ as a subcategory of $\modR$.

math.AC↗
arXiv2003

Modules of G-dimension zero over local rings with the cube of maximal ideal being zero

Let $(R, \m)$ be a commutative Noetherian local ring with $\m^3 =(0)$. We give a condition for $R$ to have a non-free module of G-dimension zero. We shall also construct a family of non-isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of projective space. We shall finally show that the subcategory consisting of modules of G-dimension zero over $R$ is not necessarily a contravariantly finite subcategory in the category of finitely generated $R$-modules.

math.AC↗