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,δ], and P∩R is a prime...

Full description

Saved in:
Bibliographic Details
Published in:Algebra and Discrete Mathematics
Date:2011
Main Author: Bhat, V.K.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/154862
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-154862
record_format dspace
spelling Bhat, V.K.
2019-06-16T05:49:02Z
2019-06-16T05:49:02Z
2011
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.
1726-3255
2000 Mathematics Subject Classification:16S36, 16N40, 16P40, 16S32
https://nasplib.isofts.kiev.ua/handle/123456789/154862
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.
The author would like to express his sincere thanks to the referee for his suggestions
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
On Pseudo-valuation rings and their extensions
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On Pseudo-valuation rings and their extensions
spellingShingle On Pseudo-valuation rings and their extensions
Bhat, V.K.
title_short On Pseudo-valuation rings and their extensions
title_full On Pseudo-valuation rings and their extensions
title_fullStr On Pseudo-valuation rings and their extensions
title_full_unstemmed On Pseudo-valuation rings and their extensions
title_sort on pseudo-valuation rings and their extensions
author Bhat, V.K.
author_facet Bhat, V.K.
publishDate 2011
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description 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
url https://nasplib.isofts.kiev.ua/handle/123456789/154862
citation_txt 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.
work_keys_str_mv AT bhatvk onpseudovaluationringsandtheirextensions
first_indexed 2025-12-07T20:57:59Z
last_indexed 2025-12-07T20:57:59Z
_version_ 1850884572191916032