DIAGONALIZATION OF REGULAR MATRICES OVER EXCHANGE RINGS

Huanyin CHEN

Makale detayları

DIAGONALIZATION OF REGULAR MATRICES OVER EXCHANGE RINGS

Yazarlar:

Huanyin CHEN

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.6 Issue 6, pp.107-114

Belge Tipi:

Makale

Yayın Tarihi:

11/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718401

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

In this paper, we establish several necessary and sufficient conditions under which every regular matrix admits a diagonal reduction. We prove that every regular matrix over an exchange ring R admits diagonal reduction if and only if for any m, n ∈ N (m ≥ n + 1) and any regular X ∈ Mm×n(R), ³X 0m×(m−n)´∈ Mm(R) is unit-regular if and only if for any m, n ∈ N (m ≥ n+ 1) and any regular X ∈ Mm×n(R), there exist an idempotent E ∈ Mm(R) and a completed U ∈ Mm×n(R) such that X = EU if and only if for any idempotents e ∈ R, f ∈ M2(R), ϕ : eR ∼= f(2R) implies that there exists a completed u ∈ 2R such that ϕ(e) = ue = fu. These shows that diagonal reduction over exchange rings behaves like stable ranges.

Makale detayları

DIAGONALIZATION OF REGULAR MATRICES OVER EXCHANGE RINGS

Yazarlar: Huanyin CHEN

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2009 Vol.6 Issue 6, pp.107-114

Belge Tipi: Makale

Yayın Tarihi: 11/2009

Belge Dili: Türkçe

Document ID (Org No.): 2000718401

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

Huanyin CHEN

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.6 Issue 6, pp.107-114

Belge Tipi:

Makale

Yayın Tarihi:

11/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718401

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048