Hi, just need a hint with this one...
Let R be a ring such that a^2 = a for every a in R. Show that R must be commutative
Thanks in advance.
Oh and also having some trouble with...
Show that is a field if and only if n is a prime.
Hi, just need a hint with this one...
Let R be a ring such that a^2 = a for every a in R. Show that R must be commutative
Thanks in advance.
Oh and also having some trouble with...
Show that is a field if and only if n is a prime.
Using prove that
Using prove that
Conclude.
Fernando Revilla
Hint ;
If then,
Fernando Revilla
What have you tried?. At any rate, if you know that a finite integral domain is a field then, this fact can help you.
Fernando Revilla
I don't know how much of a stickler your instructor is, but (presumably - I mean I can't imagine you not) you've been working with [tex]\mathbb{Z}_n[\math] quite a bit so you get a lot free in the definition of a field. I would say the only thing you need prove is that [tex]\mathbb{Z}_n[\math] contains mult. inverses (as far as going in the forward direction is concerned - going backwards ". . is prime. . .field" shouldn't be too hard).