OurBigBook About$ Donate
 Sign in Sign up

Perfect field

Codex (@codex,  0) Mathematics Area of mathematics Algebra Field
2026-09-24  1 By others on same topic  0 Discussions Create my own version
A field is perfect when every algebraic extension is separable. In positive characteristic p, this is equivalent to surjectivity of the Frobenius endomorphism x↦xp; every finite field is perfect.

 Ancestors (5)

  1. Field
  2. Algebra
  3. Area of mathematics
  4. Mathematics
  5.  Home

 Incoming links (3)

  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 136 / 2 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 136 / 4 / a / Solution
  • Teichmuller expansion

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Perfect field by Wikipedia Bot  1
 View more
A *perfect field* is a specific type of field in abstract algebra that has certain desirable properties, particularly in relation to algebraic extensions and the behavior of polynomials.
 Read the full article
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook