On rings over which every finitely generated module is a direct sum of cyclic modules

M. BEHBOODİ; G. Behboodi ESKANDARİ

Makale detayları

On rings over which every finitely generated module is a direct sum of cyclic modules

Yazarlar:

M. BEHBOODİ | G. Behboodi ESKANDARİ

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 5, pp.1335-1342

Belge Tipi:

Makale

Yayın Tarihi:

9/2016

Belge Dili:

İngilizce

Document ID (Org No.):

2000452439

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

In this paper we study (non-commutative) rings R over which every finitely generated left module is a direct sum of cyclic modules (called left FGC-rings). The commutative case was a well-known problem studied and solved in 1970s by various authors. It is shown that a Noetherian local left FGC-ring is either an Artinian principal left ideal ring, or an Artinian principal right ideal ring, or a prime ring over which every two-sided ideal is principal as a left and a right ideal. In particular, it is shown that a Noetherian local duo-ring R is a left FGCring if and only if R is a right FGC-ring, if and only if, R is a principal ideal ring.

Makale detayları

On rings over which every finitely generated module is a direct sum of cyclic modules

Yazarlar: M. BEHBOODİ | G. Behboodi ESKANDARİ

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 5, pp.1335-1342

Belge Tipi: Makale

Yayın Tarihi: 9/2016

Belge Dili: İngilizce

Document ID (Org No.): 2000452439

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

M. BEHBOODİ | G. Behboodi ESKANDARİ

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2016 Vol.45 Issue 5, pp.1335-1342

Belge Tipi:

Makale

Yayın Tarihi:

9/2016

Belge Dili:

İngilizce

Document ID (Org No.):

2000452439

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X