$S$-cotorsion modules and dimensions

Refat Abelmawla Khaled Assaad; Xiaolei Zhang

Article Details

$S$-cotorsion modules and dimensions

Authors:

Refat Abelmawla Khaled Assaad | Xiaolei Zhang

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 2, pp.410-419

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001286623

pISSN:

2651-477X

Keywords:

Abstract:

 Let R be a ring, S a multiplicative subset of R. An R-module M is said to be u-S-flat u- always abbreviates uniformly if rm TorR_1 M, N is u-S-torsion R-module for all R-modules N. In this paper, we introduce and study the concept of S-cotorsion module which is in some way a generalization of the notion of cotorsion module. An R-module M is said to be S-cotorsion if rm Ext1_RF,M0 for any u-S-flat module F. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the S-cotorsion dimensions of modules and rings. The relations between the introduced dimensions and other classical homological dimensions are discussed. As applications, we give a new upper bound on the global dimension of rings.

 Let R be a ring, S a multiplicative subset of R. An R-module M is said to be u-S-flat u- always abbreviates uniformly if rm TorR_1 M, N is u-S-torsion R-module for all R-modules N. In this paper, we introduce and study the concept of S-cotorsion module which is in some way a generalization of the notion of cotorsion module. An R-module M is said to be S-cotorsion if rm Ext1_RF,M0 for any u-S-flat module F. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the S-cotorsion dimensions of modules and rings. The relations between the introduced dimensions and other classical homological dimensions are discussed. As applications, we give a new upper bound on the global dimension of rings.

 Let R be a ring, S a multiplicative subset of R. An R-module M is said to be u-S-flat u- always abbreviates uniformly if rm TorR_1 M, N is u-S-torsion R-module for all R-modules N. In this paper, we introduce and study the concept of S-cotorsion module which is in some way a generalization of the notion of cotorsion module. An R-module M is said to be S-cotorsion if rm Ext1_RF,M0 for any u-S-flat module F. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the S-cotorsion dimensions of modules and rings. The relations between the introduced dimensions and other classical homological dimensions are discussed. As applications, we give a new upper bound on the global dimension of rings.

 Let R be a ring, S a multiplicative subset of R. An R-module M is said to be u-S-flat u- always abbreviates uniformly if rm TorR_1 M, N is u-S-torsion R-module for all R-modules N. In this paper, we introduce and study the concept of S-cotorsion module which is in some way a generalization of the notion of cotorsion module. An R-module M is said to be S-cotorsion if rm Ext1_RF,M0 for any u-S-flat module F. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the S-cotorsion dimensions of modules and rings. The relations between the introduced dimensions and other classical homological dimensions are discussed. As applications, we give a new upper bound on the global dimension of rings.

Article Details

$S$-cotorsion modules and dimensions

Authors:

Refat Abelmawla Khaled Assaad | Xiaolei Zhang

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 2, pp.410-419

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001286623

pISSN:

2651-477X

S-cotorsion module

u-S-flat module

S-cotorsion dimension

global S-cotorsion dimension

Issues

Article Details

$S$-cotorsion modules and dimensions

Authors: Refat Abelmawla Khaled Assaad | Xiaolei Zhang

Publisher: Hacettepe University

Main Topics: Mathematical Sciences

Journal: Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 2, pp.410-419

Document Type: Article

Publication Date: 3/2023

Document Language: English

Document ID (Org No.): 2001286623

pISSN: 2651-477X

S-cotorsion module

u-S-flat module

S-cotorsion dimension

global S-cotorsion dimension

Issues

Authors:

Refat Abelmawla Khaled Assaad | Xiaolei Zhang

Publisher:

Hacettepe University

Main Topics:

Mathematical Sciences

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.52 Issue 2, pp.410-419

Document Type:

Article

Publication Date:

3/2023

Document Language:

English

Document ID (Org No.):

2001286623

pISSN:

2651-477X