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November 22nd, 2013, 08:49 AM   #1
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ring fraction.

If r in R a non empty element such that is not a zero divisor . Prove that is not a zero divisor with n in N.
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November 22nd, 2013, 09:05 AM   #2
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Re: ring fraction.

Can you prove that the same is true for r^2? Then inductively apply for the rest of the exponents?
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November 25th, 2013, 05:11 AM   #3
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Re: ring fraction.

I'm not sure, but If r is a real number not equal to 1, then for every n>=0 , then , r^0 + r^1 +......+r^n= (1-r^(n+1) / (1-r)

if you consider this? is valid?

Now , how i use the hypotesis ? : If r in R a non empty element such that is not a zero divisor

I dont understand
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November 25th, 2013, 05:46 AM   #4
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Re: ring fraction.

Quote:
Originally Posted by sebaflores
I'm not sure, but If r is a real number not equal to 1, then for every n>=0 , then , r^0 + r^1 +......+r^n= (1-r^(n+1) / (1-r)
Too complicated, can be false too, I haven't checked.

Try using the fact that r is a zero-divisor if a * r of r * b is 0 for some non zero a, b in R. So, what if r is not a zero-divisor? Can you formally state what is the definition of an element that is not a zero-divisor?
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