INC-EXTENSIONS AMID ZERO-DIVISORS

David E. DOBBS; Jay SHAPİRO

Makale detayları

INC-EXTENSIONS AMID ZERO-DIVISORS

Yazarlar:

David E. DOBBS | Jay SHAPİRO

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2010 Vol.7 Issue 7, pp.102-109

Belge Tipi:

Makale

Yayın Tarihi:

5/2010

Belge Dili:

Türkçe

Document ID (Org No.):

2000718385

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

All rings considered are commutative with identity. Let R be a complemented ring with integral closure R0 (in its total quotient ring K). Then R ⊆ S satisfies INC for each overring S of R (inside K) if and only if R0 is a Prüfer ring. If R0 is a Prüfer ring and T is a complemented ring that contains R as a subring such that each regular element of T is a root of a polynomial in R[X] with a regular coefficient and T is torsion-free over R, then R ⊆ T satisfies INC. As a consequence, a new generalization for rings with nontrivial zero-divisors is found of Pr¨ufer’s result on the integral closure of a Prüfer domain in a field extension of the quotient field.

Makale detayları

INC-EXTENSIONS AMID ZERO-DIVISORS

Yazarlar: David E. DOBBS | Jay SHAPİRO

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2010 Vol.7 Issue 7, pp.102-109

Belge Tipi: Makale

Yayın Tarihi: 5/2010

Belge Dili: Türkçe

Document ID (Org No.): 2000718385

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

David E. DOBBS | Jay SHAPİRO

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2010 Vol.7 Issue 7, pp.102-109

Belge Tipi:

Makale

Yayın Tarihi:

5/2010

Belge Dili:

Türkçe

Document ID (Org No.):

2000718385

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048