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## #1 2010-04-16 06:01:47

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

### Abstract Algebra - Ring [extended level] =_="

(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

. What criteria must be held by
? (is it prime or un-reduced?)

Anyone can help me plz....

I am the greatest magician this century!!!

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## #2 2010-04-16 08:03:42

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

### Re: Abstract Algebra - Ring [extended level] =_="

(1) Use induction.

(2) Hint:

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## #3 2010-04-16 10:06:01

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

### Re: Abstract Algebra - Ring [extended level] =_="

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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