CHARACTERIZATIONS OF SOME CLASSES OF RINGS VIA LOCALLY SUPPLEMENTED MODULES

Farid KOURKİ; Rachid TRİBAK

doi:https://doi.org/10.24330/ieja.663060

Makale detayları

CHARACTERIZATIONS OF SOME CLASSES OF RINGS VIA LOCALLY SUPPLEMENTED MODULES

Yazarlar:

Farid KOURKİ | Rachid TRİBAK

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2020 Vol.27 Issue 27, pp.178-193

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000717915

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.663060

Özet:

 

We introduce the notion of locally supplemented modules (i.e., modules for which every finitely generated submodule is supplemented). We show that a module MMM is locally supplemented if and only if MMM is a sum of local submodules. We characterize several classes of rings in terms of locally supplemented modules. Among others, we prove that a ring RRR is a Camillo ring if and only if every finitely embedded RRR-module is locally supplemented. It is also shown that a ring RRR is a Gelfand ring if and only if every RRR-module having a finite Goldie dimension is locally supplemented.

Makale detayları

CHARACTERIZATIONS OF SOME CLASSES OF RINGS VIA LOCALLY SUPPLEMENTED MODULES

Yazarlar: Farid KOURKİ | Rachid TRİBAK

Yayıncı: Abdullah HARMANCI

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Algebra 2020 Vol.27 Issue 27, pp.178-193

Belge Tipi: Makale

Yayın Tarihi: 1/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000717915

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.663060

Sayı

Yazarlar:

Farid KOURKİ | Rachid TRİBAK

Yayıncı:

Abdullah HARMANCI

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Algebra 2020 Vol.27 Issue 27, pp.178-193

Belge Tipi:

Makale

Yayın Tarihi:

1/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000717915

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.663060