Field theory and polynomials Transcendental extensions Concept
Algebraic independence
Summary
A set of elements of a field extension is algebraically independent if no nonzero polynomial relation with coefficients in the base field holds among them. It is the analogue for polynomials of linear independence for linear combinations. A single element is algebraically independent exactly when it is transcendental. Maximal algebraically independent sets are transcendence bases.
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| Tag | KV4PT6KW10 |
|---|---|
| URI | m2://KV4PT6KW10 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 12F20 |
| Same as | |
| Changed | 2 November 2026 |
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