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Let $L$ be a field extension of a field $K$ . Two elements $\alpha, \beta$ of $L$ are 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 algebraically independent.
More generally, elements $\alpha_1,\ldots,\alpha_n\in L$ are said to be algebraically dependent if there exists a non-zero polynomial $f(x_1,\ldots,x_n)\in K[x_1,\ldots,x_n]$ such that $f(\alpha_1,\alpha_2,\ldots,\alpha_n)=0$ . If no such polynomial exists, the collection of $\alpha$ 's are said to be algebraically independent.
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