ON NEAR PSEUDO-VALUATION RINGS AND THEIR EXTENSIONS

V. K. BHAT

Makale detayları

ON NEAR PSEUDO-VALUATION RINGS AND THEIR EXTENSIONS

Yazarlar:

V. K. BHAT

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.70-77

Belge Tipi:

Makale

Yayın Tarihi:

5/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718409

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048

Özet:

 

Recall that a commutative ring R is said to be a pseudo-valuation ring (PVR) if every prime ideal of R is strongly prime. We say that a commutative ring R is near pseudo-valuation ring if every minimal prime ideal is a strongly prime ideal.
 We also recall that a prime ideal P of a ring R is said to be divided if it is comparable (under inclusion) to every ideal of R. A ring R is called a divided ring if every prime ideal of R is divided.
 Let R be a commutative ring, σ an automorphism of R and δ a σ-derivation of R. We say that a prime ideal P of R is δ-divided if it is comparable (under inclusion) to every σ-stable and δ- invariant ideal I of R. A ring R is called a δ-divided ring if every prime ideal of R is δ-divided. We say that a ring R is almost δ-divided ring if every minimal prime ideal of R is δ-divided. With this we prove the following:
 Let R be a commutative Noetherian Q-algebra (Q is the field of rational numbers), σ and δ as usual. Then:
 (1) If R is a near pseudo valuation σ(∗)- ring, then R[x; σ, δ] is a near pseudo valuation ring.
 (2) If R is an almost δ-divided σ(∗)-ring, then R[x; σ, δ] is an almost divided ring.

Makale detayları

ON NEAR PSEUDO-VALUATION RINGS AND THEIR EXTENSIONS

Yazarlar: V. K. BHAT

Yayıncı: Abdullah HARMANCI

Dergi: International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.70-77

Belge Tipi: Makale

Yayın Tarihi: 5/2009

Belge Dili: Türkçe

Document ID (Org No.): 2000718409

Sıklık: Aylık

eISSN: 1306-6048

pISSN: 1306-6048

Sayı

Yazarlar:

V. K. BHAT

Yayıncı:

Abdullah HARMANCI

Dergi:

International Electronic Journal of Algebra 2009 Vol.5 Issue 5, pp.70-77

Belge Tipi:

Makale

Yayın Tarihi:

5/2009

Belge Dili:

Türkçe

Document ID (Org No.):

2000718409

Sıklık:

Aylık

eISSN:

1306-6048

pISSN:

1306-6048