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

(1)

Given Integral domain R and

a) not unit, is called prime element

if a|bc implies a|b or a|c.

Show that a is prime element iff <a> is prime ideal

b) not unit, is said un-reduced

if a = bc implies b is unit or c is unit.

Show that if p is prime and for some i.

(2)

If

Anyone can help me plz....

I am the greatest magician this century!!!

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

(1) Use induction.

(2) Hint:

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

For (1a), remember the phrase "to contain is to divide". If (a) contains (b), then a divides 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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