radical
Let be a field and be algebraic (http://planetmath.org/Algebraic) over . Then is a radical over if there exists a positive integer with .
Note that, if is a field extension and is a radical over , then is automatically a radical over .
Following are some examples of radicals:
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1.
All numbers of the form , where is a positive integer and and are integers with are radicals over .
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2.
The number is a radical over since .
Title | radical |
---|---|
Canonical name | Radical1 |
Date of creation | 2013-03-22 16:55:36 |
Last modified on | 2013-03-22 16:55:36 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 9 |
Author | Wkbj79 (1863) |
Entry type | Definition |
Classification | msc 12F05 |
Classification | msc 12F10 |
Related topic | RadicalExtension |
Related topic | NthRoot |
Related topic | SolvableByRadicals |
Related topic | Radical6 |