Homological dimensions of complexes related to cotorsion pairs

Chongqing WEI; Limin WANG; Husheng QIAO

Makale detayları

Homological dimensions of complexes related to cotorsion pairs

Yazarlar:

Chongqing WEI | Limin WANG | Husheng QIAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 3, pp.401-418

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747334

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

 

Let (A, B) be a cotorsion pair in R-Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg-projective resolution and dg-injective resolution, respectively. As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.

Makale detayları

Homological dimensions of complexes related to cotorsion pairs

Yazarlar:

Chongqing WEI | Limin WANG | Husheng QIAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 3, pp.401-418

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747334

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Cotorsion pairs

A dimension of complexes

B dimension of complexes

Sayı

Makale detayları

Homological dimensions of complexes related to cotorsion pairs

Yazarlar: Chongqing WEI | Limin WANG | Husheng QIAO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2014 Vol.38 Issue 3, pp.401-418

Belge Tipi: Makale

Yayın Tarihi: 5/2014

Belge Dili: Türkçe

Document ID (Org No.): 2000747334

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Cotorsion pairs

A dimension of complexes

B dimension of complexes

Sayı

Yazarlar:

Chongqing WEI | Limin WANG | Husheng QIAO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2014 Vol.38 Issue 3, pp.401-418

Belge Tipi:

Makale

Yayın Tarihi:

5/2014

Belge Dili:

Türkçe

Document ID (Org No.):

2000747334

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098