Nilpotent elements and reduced rings

Junchao WEI; Libin LI

Makale detayları

Nilpotent elements and reduced rings

Yazarlar:

Junchao WEI | Libin LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.341-353

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747999

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In this paper, we show the following results: (1) R is a  min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in  MEl(R); (2) Quasi-normal rings, NI rings and weakly reversible rings  are all min-leftsemicentral ring; (3) R is left MC2 ring if and only  if aRe=0 implies eRa=0 for all e \in MEl(R) and a \in R if and only  if every projective simple left R-module is MUP-injective; (4) R is  reduced if and only if R is n-regular and quasi-normal if and only if  R is n-regular and weakly reversible; (5) R is strongly regular if and  only if R is regular and quasi-normal if and only if R is regular and  weakly reversible.

 

In this paper, we show the following results: (1) R is a  min-leftsemicentral ring if and only if eR(1-e)Re=0 for all e \in  MEl(R); (2) Quasi-normal rings, NI rings and weakly reversible rings  are all min-leftsemicentral ring; (3) R is left MC2 ring if and only  if aRe=0 implies eRa=0 for all e \in MEl(R) and a \in R if and only  if every projective simple left R-module is MUP-injective; (4) R is  reduced if and only if R is n-regular and quasi-normal if and only if  R is n-regular and weakly reversible; (5) R is strongly regular if and  only if R is regular and quasi-normal if and only if R is regular and  weakly reversible.

Makale detayları

Nilpotent elements and reduced rings

Yazarlar:

Junchao WEI | Libin LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.341-353

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747999

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Min-leftsemicentral rings

quasi-normal rings. NCI rings

weakly reversible rings

left MC2 rings

directly finite rings

regular rings

Sayı

Makale detayları

Nilpotent elements and reduced rings

Yazarlar: Junchao WEI | Libin LI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.341-353

Belge Tipi: Makale

Yayın Tarihi: 1/2011

Belge Dili: Türkçe

Document ID (Org No.): 2000747999

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Min-leftsemicentral rings

quasi-normal rings. NCI rings

weakly reversible rings

left MC2 rings

directly finite rings

regular rings

Sayı

Yazarlar:

Junchao WEI | Libin LI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2011 Vol.35 Issue 2, pp.341-353

Belge Tipi:

Makale

Yayın Tarihi:

1/2011

Belge Dili:

Türkçe

Document ID (Org No.):

2000747999

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098