^^Campo algebrico. Corpo algebrico.

wp/Corpo_(matematica)

corpo  ≡  skew field  ≡  division ring    

campo  e' un corpo commutativo

Teo: i corpi finiti sono campi

cioe' i corpi finiti sono commutativi, o non esistono corpi finiti non commutativi.

dim: wp/Wedderburn's_little_theorem every finite domain is a field.

 

Examples first

credits: gowers/my-favourite-pedagogical-principle-examples-first

ℕ ℤ ℚ ℝ ℂ

ℕ ℤ       are not filds

ℚ ℝ ℂ   are fields

Subfields of ℂ and superfields of ℚ

all complex nr of the form a+b√-3  a,b rational. Denoted ℚ(√-3).

(All the field properties are very easily verified, with the exception of the existence of multiplicative inverses: but even that is a simple exercise.)

Finite fields

of which the simplest cases are obtained by taking a prime p and the set of all integers modulo p.

(Here again the only field axiom that is not almost trivial to verify is the existence of multiplicative inverses — for that one needs Euclid’s algorithm.)

 

Deane Yang Says: October 25, 2007 at 2:17 am

When I was young, I did most of my learning alone. Now that I am older, I know better. I encourage everyone to do as much learning as possible in collaboration with others. Working seminars on topics of common interest are very powerful means of learning.

Reid Says: October 26, 2007 at 2:47 am

high-schools have become a place where false self-esteem is developed, not education

Links

ℕ ℤ ℚ ℝ ℂ

 

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