Field theory and polynomials Transcendental extensions Concept
Transcendence basis
Summary
A transcendence basis of a field extension is a set of algebraically independent elements such that is algebraic over . It plays the role that a basis plays for a vector space, with polynomial relations in place of linear ones. Every extension has one, and all of them have the same cardinality, the transcendence degree.
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About this page
| Tag | E45PA267S4 |
|---|---|
| URI | m2://E45PA267S4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 12F20 |
| Changed | 2 November 2026 |
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Used by
- Steinitz's theorem on algebraically closed fields
- Function field
- Transcendence degree
- Separably generated extension
- Existence of transcendence bases