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| Title of object: |
algebraically dependent |
| Canonical Name: |
AlgebraicallyDependent |
| Type: |
Definition |
| Created on: |
2003-09-25 17:57:50 |
| Modified on: |
2004-05-22 18:26:13 |
| Classification: |
msc:12F05 |
| Defines: |
algebraically independent, algebraic dependence, algebraic independence |
Revision comment (for changes between this and next version):
| Changes for correction #4437 ('minor'). |
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Content:
| Let $L$ be an field extension of a field $K$. Two elements $\alpha, \beta$ of $L$ are \emph{algebraically dependent} if there exists a non-zero polynomial $f(x,y)\in K[x,y]$ such that $f(\alpha,\beta)=0$. If no such polynomial exists, $\alpha$ and $\beta$ are said to be \emph{algebraically independent}. |
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