Word.ws English Dictionary

Ax-Kochen theorem

Ax-Kochen theorem proper noun: a theorem stating that for each positive integer d there is a finite set Y_d of prime numbers, such that if p is any prime not in Y_d then every homogeneous polynomial of degree d over the p-adic numbers in at least d²+1 variables has a nontrivial zero.

Proper noun

the Ax-Kochen theorem

  1. A theorem stating that for each positive integer d there is a finite set Y_d of prime numbers, such that if p is any prime not in Y_d then every homogeneous polynomial of degree d over the p-adic numbers in at least d²+1 variables has a nontrivial zero.

Origin of Ax-Kochen theorem

Named after James Ax and Simon B. Kochen.

Questions about Ax-Kochen theorem

What does Ax-Kochen theorem mean?
Ax-Kochen theorem means a theorem stating that for each positive integer d there is a finite set Y_d of prime numbers, such that if p is any prime not in Y_d then every homogeneous polynomial of degree d over the p-adic numbers in at least d²+1 variables has a nontrivial zero.
What part of speech is Ax-Kochen theorem?
Ax-Kochen theorem is a proper noun.

Words near Ax-Kochen theorem in the dictionary

  1. ax
  2. ax head
  3. ax heads
  4. ax to grind
  5. Ax-Grothendieck theorem
  6. Ax-Kochen theorem
  7. axal
  8. axanthic
  9. axanthine
  10. axanthism
  11. axanthopsia

Source and license

Adapted from Wiktionary: Ax-Kochen theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “Ax-Kochen theorem.” Word.ws, https://word.ws/ax-kochen_theorem. Based on Wiktionary, CC BY-SA 4.0.