perfect field
Word Rarity
Uncommon
Frequency: Zipf frequency 4.92 in modern English
23
Scrabble Score
12
Letters
4
Syllables
9
Unique Chars
Meaning
noun
A field K such that every irreducible polynomial over K has distinct roots.
Example Sentences
- "1984, Julio R. Bastida, Field Extensions and Galois Theory, Cambridge University Press, Addison-Wesley, page 10, If K is a perfect field of prime characteristic p, and if n is a nonnegative integer, then the mapping α→α from K to K is an automorphism."
- "So far this stronger conjecture has been proved by Nazarova and Roiter over algebraically closed fields, and subsequently by Ringel over perfect fields."
- "a) K is a perfect field; b) any irreducible polynomial of K[X] is separable; c) any element of an algebraic closure of K is separable over K; d) any algebraic extension of K is separable; e) for any finite extension K→L, the number of K-homomrphisms from K to an algebraically closed extension of K is equal to [L:K]. Corollary 3.1.8. Any algebraic extension of a perfect field is again a perfect field."