Gorenstein Projective Precovers

Estrada, Sergio; Iacob, Alina; Yeomans, Katelyn

doi:10.1007/s00009-016-0822-5

Cited by 15 publications

(15 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 1. We showed in [8] Proof. By Proposition 10 above, if DP is covering, then every flat module has a projective cover.…”

Section: R-module}mentioning

confidence: 92%

Projectively coresolved Gorenstein flat and ding projective modules

Iacob

2020

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

We give necessary and sufficient conditions in order for the class of projectively coresolved Gorenstein flat modules, PGF , (respectively that of projectively coresolved Gorenstein B flat modules, PGF B ) to coincide with the class of Ding projective modules (DP). We show that PGF = DP if and only if every Ding projective module is Gorenstein flat. This is the case if the ring R is coherent for example. We include an example to show that the coherence is a sufficient, but not a necessary condition in order to have PGF = DP. We also show that PGF = DP over any ring R of finite weak Gorenstein global dimension (this condition is also sufficient, but not necessary). We prove that if the class of Ding projective modules, DP, is covering then the ring R is perfect. And we show that, over a coherent ring R, the converse also holds. We also give necessary and sufficient conditions in order to have PGF = GP, where GP is the class of Gorenstein projective modules.2010 MSC: 16E05, 16E10.

show abstract

“…Example 1. We showed in [8] Proof. By Proposition 10 above, if DP is covering, then every flat module has a projective cover.…”

Section: R-module}mentioning

confidence: 92%

Projectively coresolved Gorenstein flat and ding projective modules

Iacob

2020

Communications in Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…Examples include the classes of modules which are flat, Gorenstein projective and Gorenstein flat. A number of these results can be found in [1,2,6,7,8,14,19,26].…”

Section: Introductionmentioning

confidence: 92%

“…But for arbitrary rings this is still an open question. Work on this problem can be seen in [2,7,8,14,19] for instance.…”

Section: Introductionmentioning

confidence: 99%

Special precovering classes in comma categories

Zhu

2019

Preprint

View full text Add to dashboard Cite

Let T be a right exact functor from an abelian category B into another abelian category A . Then there exists a functor p from the product category A × B to the comma category (T ↓ A ). In this paper, we study the property of the extension closure of some classes of objects in (T ↓ A ), the exactness of the functor p and the detail description of orthogonal classes of a given class induced by p. Moreover, we characterize when special precovering classes in abelian categories A and B can induce special precovering classes in (T ↓ A ). As an application, we prove that under suitable cases, the class of Gorenstein projective left Λ-modules over a triangular matrix ring Λ = R M O S is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering. Consequently, we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them.

show abstract

“…On the other hand, since also R is commutative with finite Krull dimension, we have that GProj(R) is special precovering (see e.g. [11,Proposition 6]). Thus, we are under the hypotheses of Proposition 4.6, which says that there must exist a complete hereditary cotorsion triplet (GProj(R), G, GInj(R)) in Mod(R).…”

Section: Relation Between Balanced Pairs and Cotorsion Tripletsmentioning

confidence: 99%

On some applications of balanced pairs and their relation with cotorsion triplets

Estrada,

Pérez,

Zhu

2018

Preprint

Self Cite

View full text Add to dashboard Cite

Balanced pairs appear naturally in the realm of Relative Homological Algebra associated to the balance of right derived functors of the Hom functor. A natural source to get such pairs is by means of cotorsion triplets. In this paper we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories having enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also give a short proof of the lack of balance for derived functors of Hom computed by using flat resolutions which extends the one showed by Enochs in the commutative case.

show abstract

Gorenstein Projective Precovers

Cited by 15 publications

References 22 publications

Projectively coresolved Gorenstein flat and ding projective modules

Projectively coresolved Gorenstein flat and ding projective modules

Special precovering classes in comma categories

On some applications of balanced pairs and their relation with cotorsion triplets

Contact Info

Product

Resources

About