On closed rational functions in several variables
Let K = K¯ be a field of characteristic zero. An element ϕ ∈ K(x1,... ,xn) is called a closed rational function if the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn). We prove that a rational function ϕ = f/g is closed if f and g are algebraically independent and at least one o...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/157399 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On closed rational functions in several variables / A.P. Petravchuk, O.G. Iena // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 115–124. — Бібліогр.: 10 назв. — англ. |
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Petravchuk, A.P. Iena, O.G. 2019-06-20T03:13:29Z 2019-06-20T03:13:29Z 2007 On closed rational functions in several variables / A.P. Petravchuk, O.G. Iena // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 115–124. — Бібліогр.: 10 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 26C15. https://nasplib.isofts.kiev.ua/handle/123456789/157399 Let K = K¯ be a field of characteristic zero. An element ϕ ∈ K(x1,... ,xn) is called a closed rational function if the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn). We prove that a rational function ϕ = f/g is closed if f and g are algebraically independent and at least one of them is irreducible. We also show that a rational function ϕ = f/g is closed if and only if the pencil αf + βg contains only finitely many reducible hypersurfaces. Some sufficient conditions for a polynomial to be irreducible are given. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On closed rational functions in several variables Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On closed rational functions in several variables |
| spellingShingle |
On closed rational functions in several variables Petravchuk, A.P. Iena, O.G. |
| title_short |
On closed rational functions in several variables |
| title_full |
On closed rational functions in several variables |
| title_fullStr |
On closed rational functions in several variables |
| title_full_unstemmed |
On closed rational functions in several variables |
| title_sort |
on closed rational functions in several variables |
| author |
Petravchuk, A.P. Iena, O.G. |
| author_facet |
Petravchuk, A.P. Iena, O.G. |
| publishDate |
2007 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
Let K = K¯ be a field of characteristic zero. An
element ϕ ∈ K(x1,... ,xn) is called a closed rational function if
the subfield K(ϕ) is algebraically closed in the field K(x1,... ,xn).
We prove that a rational function ϕ = f/g is closed if f and g are
algebraically independent and at least one of them is irreducible.
We also show that a rational function ϕ = f/g is closed if and
only if the pencil αf + βg contains only finitely many reducible
hypersurfaces. Some sufficient conditions for a polynomial to be
irreducible are given.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157399 |
| citation_txt |
On closed rational functions in several variables / A.P. Petravchuk, O.G. Iena // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 115–124. — Бібліогр.: 10 назв. — англ. |
| work_keys_str_mv |
AT petravchukap onclosedrationalfunctionsinseveralvariables AT ienaog onclosedrationalfunctionsinseveralvariables |
| first_indexed |
2025-12-07T20:51:05Z |
| last_indexed |
2025-12-07T20:51:05Z |
| _version_ |
1850884138826989568 |