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...
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2011
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
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irk-123456789-1548622019-06-17T01:30:33Z On Pseudo-valuation rings and their extensions Bhat, V.K. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/154862 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Bhat, V.K. |
| spellingShingle |
Bhat, V.K. On Pseudo-valuation rings and their extensions Algebra and Discrete Mathematics |
| author_facet |
Bhat, V.K. |
| author_sort |
Bhat, V.K. |
| title |
On Pseudo-valuation rings and their extensions |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT bhatvk onpseudovaluationringsandtheirextensions |
| first_indexed |
2023-05-20T17:45:25Z |
| last_indexed |
2023-05-20T17:45:25Z |
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1796154020081958912 |