ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS

Victor Camillo; W. Keith Nicholson

doi:https://doi.org/10.24330/ieja.266221

Makale detayları

ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS

Yazarlar:

Victor Camillo | W. Keith Nicholson

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2015 Vol.17 Issue 17, pp.199-214

Belge Tipi:

Makale

Yayın Tarihi:

5/2015

Belge Dili:

Türkçe

Document ID (Org No.):

2000718168

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.266221

Özet:

 

The rings in the title are studied and related to right principally
 injective rings. Many properties of these rings (called left pseudo-morphic by
 Yang) are derived, and conditions are given that an endomorphism ring is left
 pseudo-morphic. Some particular results: (1) Commutative pseudo-morphic
 rings are morphic; (2) Semiprime left pseudo-morphic rings are semisimple;
 and (3) A left and right pseudo-morphic ring satisfying (equivalent) mild
 finiteness conditions is a morphic, quasi-Frobenius ring in which every onesided
 ideal is principal. Call a left ideal L a left principal annihilator if
 L = l(a) = {r ∈ R | ra = 0} for some a ∈ R. It is shown that if R is left
 pseudo-morphic, left mininjective ring with the ACC on left principal annihilators
 then R is a quasi-Frobenius ring in which every right ideal is principal
 and every left ideal is a left principal annihilator.

Makale detayları

ON RINGS WHERE LEFT PRINCIPAL IDEALS ARE LEFT PRINCIPAL ANNIHILATORS

Yazarlar: Victor Camillo | W. Keith Nicholson

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2015 Vol.17 Issue 17, pp.199-214

Belge Tipi: Makale

Yayın Tarihi: 5/2015

Belge Dili: Türkçe

Document ID (Org No.): 2000718168

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

DOI: https://doi.org/10.24330/ieja.266221

Sayı

Yazarlar:

Victor Camillo | W. Keith Nicholson

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2015 Vol.17 Issue 17, pp.199-214

Belge Tipi:

Makale

Yayın Tarihi:

5/2015

Belge Dili:

Türkçe

Document ID (Org No.):

2000718168

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

DOI:

https://doi.org/10.24330/ieja.266221