ON VNL-RINGS AND n-VNL-RINGS

Jianlong CHEN; Zhiling YİNG

Makale detayları

ON VNL-RINGS AND n-VNL-RINGS

Yazarlar:

Jianlong CHEN | Zhiling YİNG

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.1-8

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718416

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

A ring R is called a VNL-ring if a or 1−a is regular for every a ∈ R. We call a ring R a right n-VNL-ring if whenever a1R + a2R + · · · + anR = R for some elements a1, a2, · · · , an of R, then there exists at least one element ai (von Neumann) regular. It is proven that there exists a right 2-VNL-ring but not right 3-VNL, which gives a negative answer to a question raised by Chen and Tong in 2006. We prove that R is regular iff the n × n matrix ring over R is a VNL-ring for some n ≥ 2. It is also proven that a ring R is a division ring iff R is semilocal and the 2 × 2 upper triangular matrix ring over R is a VNL-ring.

Makale detayları

ON VNL-RINGS AND n-VNL-RINGS

Yazarlar: Jianlong CHEN | Zhiling YİNG

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.1-8

Belge Tipi: Makale

Yayın Tarihi: 11/2008

Belge Dili: Türkçe

Document ID (Org No.): 2000718416

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

Jianlong CHEN | Zhiling YİNG

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2008 Vol.4 Issue 4, pp.1-8

Belge Tipi:

Makale

Yayın Tarihi:

11/2008

Belge Dili:

Türkçe

Document ID (Org No.):

2000718416

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048