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...
Збережено в:
| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2007
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| Резюме: | 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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