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
 algebraicall...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2007 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
|
| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747534001176576 |
|---|---|
| author | Petravchuk, A.P. Iena, O.G. |
| author_facet | Petravchuk, A.P. Iena, O.G. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T20:51:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157399 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T20:51:05Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On closed rational functions in several variables Petravchuk, A.P. Iena, O.G. |
| title | 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_short | On closed rational functions in several variables |
| title_sort | on closed rational functions in several variables |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157399 |
| work_keys_str_mv | AT petravchukap onclosedrationalfunctionsinseveralvariables AT ienaog onclosedrationalfunctionsinseveralvariables |