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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2011 |
| Main Author: | |
| 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 |