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#1 2007-03-20 21:03:28
- freddogtgj
- Member
- Registered: 2006-12-02
- Posts: 54
Algebra Help
I have this question that I need help in
Let R be a ring in which a^2 = a for all a ∈ R. By considering (a+b)^2,
show
(a) R is commutative;
(b) a+a = 0 for all a ∈ R.
Thanks in advance!
∈ - element of
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#2 2007-03-21 03:45:34
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Algebra Help
Do (b) first. You need (b) to prove (a)
For (a)
The result follows from (b).
Note: In any ring, −ab = (−a)b = a(−b). This can be proved from the distributive ring axiom and the fact that c·0 = 0·c = c for any element c in the ring. See this.
Last edited by JaneFairfax (2007-03-21 03:56:40)
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#3 2007-03-21 23:45:40
- freddogtgj
- Member
- Registered: 2006-12-02
- Posts: 54
Re: Algebra Help
Cool thanks! I have a similar answer using wikipedia
http://en.wikipedia.org/wiki/Boolean_ring
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