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 November 22nd, 2013, 08:49 AM #1 Newbie   Joined: Sep 2013 Posts: 17 Thanks: 0 ring fraction. If r in R a non empty element such that is not a zero divisor . Prove that $r^n$ is not a zero divisor with n in N.
 November 22nd, 2013, 09:05 AM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: ring fraction. Can you prove that the same is true for r^2? Then inductively apply for the rest of the exponents?
 November 25th, 2013, 05:11 AM #3 Newbie   Joined: Sep 2013 Posts: 17 Thanks: 0 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
November 25th, 2013, 05:46 AM   #4
Math Team

Joined: Mar 2012
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Math Focus: Number Theory
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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