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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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862749003526963200 |
|---|---|
| author | Bhat, V.K. |
| author_facet | Bhat, V.K. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T20:57:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154862 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:57:59Z |
| publishDate | 2011 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | On Pseudo-valuation rings and their extensions Bhat, V.K. |
| title | 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_short | On Pseudo-valuation rings and their extensions |
| title_sort | on pseudo-valuation rings and their extensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154862 |
| work_keys_str_mv | AT bhatvk onpseudovaluationringsandtheirextensions |