نتایج جستجو برای: f gorenstein injective module

تعداد نتایج: 372352  

Journal: :Comptes Rendus Mathematique 2021

Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings R do we have K(AC)=K(R-Inj)?”. We give an answer to such a question. As applications, obtain new homological approach unifies some well-known conditions Krause’s recollement holds, and example show there exists Gorenstein injective module is not AC-injective. also improve Neeman’s an...

Let R be a commutative noetherian ring and Γ a finite group. In this paper,we study Gorenstein homological dimensions of modules with respect to a semi-dualizing module over the group ring  . It is shown that Gorenstein homological dimensions  of an  -RΓ module M with respect to a semi-dualizing module,  are equal over R and RΓ  .

2007
E. ENOCHS S. ESTRADA J. R. GARCÍA ROZAS

In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and then describe Gorenstein injective and projective representations of barren trees.

2008
Driss Bennis

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we invest...

Journal: :Journal of Pure and Applied Algebra 2021

Let k be a fixed field of arbitrary characteristic and let ? basic connected Nakayama k-algebra without simple projective modules. In this article we prove that if V is an indecomposable finitely generated Gorenstein-projective left ?-module, then the versal deformation ring R(?,V) (in sense F. M. Bleher author) universal stable after taking syzygies. We also following result. ?=(?B0?) triangul...

2004
Francois Couchot FRANÇOIS COUCHOT

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...

2008
XIAO-WU CHEN

We prove that if a positively-graded ring R is Gorenstein and the associated torsion functor has finite cohomological dimension, then the corresponding noncommutative projective scheme Tails(R) is a Gorenstein category in the sense of [10]. Moreover, under this condition, a (right) recollement relating Gorensteininjective sheaves in Tails(R) and (graded) Gorenstein-injective R-modules is given.

2007
N. MAHDOU

In this paper, we prove that the global Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective dimension of R, and that the global Gorenstein flat dimension of R is smaller than the common value of the terms of this equality.

2014
P. H. Lima Jorge Pérez

Let (A,m) be a Noetherian local ring and F = (In)n≥0 a filtration. In this paper, we study the Gorenstein properties of the fiber cone F (F), where F is a Hilbert filtration. Suppose that F (F) and G(F) are CohenMacaulay. If in addition, the associated graded ring G(F) is Gorenstein; similarly to the I-adic case, we obtain a necessary and sufficient condition, in terms of lengths and minimal nu...

Journal: :Int. J. Math. Mathematical Sciences 2005
Paul Isaac

The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove t...

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