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**GOKILL****Member**- Registered: 2010-03-19
- Posts: 26

#1

Let F be a field, show that F[x] is the main ideal domain (ideal region)!

#2

Let R be integral domain,

a) Show that S doesn't contain zero-divisor

b) Defined , show that Rs isomorfic with the subring of Q(R)

[Q(R) is the smallest subfield containing R, called as divisor field]

#3

Suppose f is ring homomorphism from R (ring with unity element) to the ring R'.

If

Help me please

thxu

I am the greatest magician this century!!!

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

1. If you know the division algorithm works in F[x], then this proof becomes easy. Prove it's a Euclidean domain, and this implies it is a principal ideal domain.

2b "show that Rs isomorfic with the subring of Q(R)" With *a* subring of Q(R)? When you have a subset, there is always a very easy way to injectively define a map.

3 f(ab) = f(a)f(b)

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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