Torsion pairs and related modules over trivial ring extensions

Lixin Mao

Makale detayları

Torsion pairs and related modules over trivial ring extensions

Yazarlar:

Lixin Mao

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1291-1304

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329414

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 Let Rltimes M be a trivial extension of a ring R by an R-R-bimodule M. We first study how to construct torsion pairs over Rltimes M from torsion pairs over R. Some characterizations of finitely generated presented modules, flat modules and coherent rings relative to a torsion pair over Rltimes M are obtained. Then we discuss the transfers of torsion pairs over Rltimes M to R. Finally, some applications are given in Morita context rings.

 Let Rltimes M be a trivial extension of a ring R by an R-R-bimodule M. We first study how to construct torsion pairs over Rltimes M from torsion pairs over R. Some characterizations of finitely generated presented modules, flat modules and coherent rings relative to a torsion pair over Rltimes M are obtained. Then we discuss the transfers of torsion pairs over Rltimes M to R. Finally, some applications are given in Morita context rings.

 Let Rltimes M be a trivial extension of a ring R by an R-R-bimodule M. We first study how to construct torsion pairs over Rltimes M from torsion pairs over R. Some characterizations of finitely generated presented modules, flat modules and coherent rings relative to a torsion pair over Rltimes M are obtained. Then we discuss the transfers of torsion pairs over Rltimes M to R. Finally, some applications are given in Morita context rings.

 Let Rltimes M be a trivial extension of a ring R by an R-R-bimodule M. We first study how to construct torsion pairs over Rltimes M from torsion pairs over R. Some characterizations of finitely generated presented modules, flat modules and coherent rings relative to a torsion pair over Rltimes M are obtained. Then we discuss the transfers of torsion pairs over Rltimes M to R. Finally, some applications are given in Morita context rings.

Makale detayları

Torsion pairs and related modules over trivial ring extensions

Yazarlar: Lixin Mao

Yayıncı: Hacettepe University

Ana Başlıklar: Mathematical Sciences

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1291-1304

Belge Tipi: Makale

Yayın Tarihi: 10/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001329414

pISSN: 2651-477X

torsion pair

trivial ring extension

Morita context ring

Sayı

Yazarlar:

Lixin Mao

Yayıncı:

Hacettepe University

Ana Başlıklar:

Mathematical Sciences

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 5, pp.1291-1304

Belge Tipi:

Makale

Yayın Tarihi:

10/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001329414

pISSN:

2651-477X