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Everything about Primitive element theorem
Field theory theorem
In field theory, the primitive element theorem states that every finite separable field extension is simple, i.e. generated by a single element. This theorem implies in particular that all algebraic number fields over the rational numbers, and all extensions in which both fields are finite, are simple. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Primitive element theoremA 5-minute orientation
- Skim a recent paper: Spectral theory of B-Weyl elements and the generalized Weyl's theorem in primitive C*-algebraInfluential work since 2022
- Pick up a classic book: Cartesian meditationsThe most-reprinted book on the subject
- Read the landmark paper: On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie AlgebrasCited 10 times
- Go sideways: Normal basisA closely related topic
- Go sideways: Field traceA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras
The primitive element theorem for differential fields with zero derivation on the ground field
On the Theorem on the Primitive Element
On the primitive element and normal basis theorems
A primitive element theorem for fields with commuting derivations and automorphisms
An effective version of the primitive element theorem
The Theorem of the Primitive Element
Generalizations of the primitive element theorem
🆕 Influential since 2022
đź“š Books worth reading
Cartesian meditationsEdmund Husserl, Dorion Cairns · 1960
Discrete mathematicsNorman Biggs · 1985- 📕How to be a quantitative ecologistJason Matthiopoulos · 2011
Computer algorithmsEllis Horowitz · 1997
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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