On Pseudo-valuation rings and their extensions

Let R be a commutative Noetherian Q-algebra (Q
 is the field of rational numbers). Let σ be an automorphism of R and δ a σ-derivation of R. We define a δ-divided ring and prove the following:
 
 (1)If R is a pseudo-valuation ring such that x∉P for any prime ideal P of R[x;σ...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2011
ISSN:1726-3255
1. Verfasser: Bhat, V.K.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2011
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/154862
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:On Pseudo-valuation rings and their extensions / V.K. Bhat // Algebra and Discrete Mathematics. — 2011. — Vol. 12, № 2. — С. 25–30. — Бібліогр.: 14 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung:Let R be a commutative Noetherian Q-algebra (Q
 is the field of rational numbers). Let σ be an automorphism of R and δ a σ-derivation of R. We define a δ-divided ring and prove the following:
 
 (1)If R is a pseudo-valuation ring such that x∉P for any prime ideal P of R[x;σ,δ], and P∩R is a prime ideal of R with σ(P∩R)=P∩R and δ(P∩R)⊆P∩R, then R[x;σ,δ] is also a pseudo-valuation ring.
 
 (2)If R is a δ-divided ring such that x∉P for any prime ideal P of R[x;σ,δ], and P∩R is a prime ideal of R with σ(P∩R)=P∩R and δ(P∩R)⊆P∩R, then R[x;σ,δ] is also a δ-divided ring.
ISSN:1726-3255