corpo ≡ skew field ≡ division ring
campo e' un corpo commutativo
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.
credits: gowers/my-favourite-pedagogical-principle-examples-first
ℕ ℤ are not filds
ℚ ℝ ℂ are fields
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.)
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