Lesson plan
Algebraic function field
In mathematics, an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has transcendence degree n over k . Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K=k(x_1,\dots,x_n) of rational functions in n variables over k .
Article summary
In mathematics, an algebraic function field (often abbreviated as function field) of n variables over a field k is a finitely generated field extension K/k which has transcendence degree n over k . Equivalently, an algebraic function field of n variables over k may be defined as a finite field extension of the field K=k(x_1,\dots,x_n) of rational functions in n variables over k .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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