On the kernels of higher R-derivations of R[x1, ... xn]
Let R be an integral domain and A = R[x1, . . . , xn] be the polynomial ring in n variables. In this article, we study the kernel of higher R-derivation D of A. It is shown that if R is a HCF ring and tr. degR(Aᴰ) ≤ 1 then Aᴰ = R[f] for some f ∈ A.
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/188750 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On the kernels of higher R-derivations of R[x1, ... xn] / S. Kour // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 236-240. — Бібліогр.: 9 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862686957951254528 |
|---|---|
| author | Kour, S. |
| author_facet | Kour, S. |
| citation_txt | On the kernels of higher R-derivations of R[x1, ... xn] / S. Kour // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 236-240. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | Let R be an integral domain and A = R[x1, . . . , xn] be the polynomial ring in n variables. In this article, we study the kernel of higher R-derivation D of A. It is shown that if R is a HCF ring and tr. degR(Aᴰ) ≤ 1 then Aᴰ = R[f] for some f ∈ A.
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| first_indexed | 2025-12-07T16:05:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188750 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:05:25Z |
| publishDate | 2021 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Kour, S. 2023-03-14T17:00:36Z 2023-03-14T17:00:36Z 2021 On the kernels of higher R-derivations of R[x1, ... xn] / S. Kour // Algebra and Discrete Mathematics. — 2021. — Vol. 32, № 2. — С. 236-240. — Бібліогр.: 9 назв. — англ. 1726-3255 DOI:10.12958/adm1236 2020 MSC: 13N15, 13C99 https://nasplib.isofts.kiev.ua/handle/123456789/188750 Let R be an integral domain and A = R[x1, . . . , xn] be the polynomial ring in n variables. In this article, we study the kernel of higher R-derivation D of A. It is shown that if R is a HCF ring and tr. degR(Aᴰ) ≤ 1 then Aᴰ = R[f] for some f ∈ A. This research is supported by DST-INSPIRE grant IFA-13/MA-30. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the kernels of higher R-derivations of R[x1, ... xn] Article published earlier |
| spellingShingle | On the kernels of higher R-derivations of R[x1, ... xn] Kour, S. |
| title | On the kernels of higher R-derivations of R[x1, ... xn] |
| title_full | On the kernels of higher R-derivations of R[x1, ... xn] |
| title_fullStr | On the kernels of higher R-derivations of R[x1, ... xn] |
| title_full_unstemmed | On the kernels of higher R-derivations of R[x1, ... xn] |
| title_short | On the kernels of higher R-derivations of R[x1, ... xn] |
| title_sort | on the kernels of higher r-derivations of r[x1, ... xn] |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188750 |
| work_keys_str_mv | AT kours onthekernelsofhigherrderivationsofrx1xn |