On closed rational functions in several variables
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On closed rational functions in several variables
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| Creator |
Petravchuk, A.P.
Iena, O.G. |
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| 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. |
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| Date |
2019-06-20T03:13:29Z
2019-06-20T03:13:29Z 2007 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/157399 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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